Sequences

392,541 sequences

a(n) = T(2n, n-2), T given by A026758.A026761
a(n) = T(2n, n-2), T given by A026758.
a(n) = T(2n-1,n-1), T given by A026758. Also T(2n+1,n+1), T given by A026747.A026762
a(n) = T(2n-1,n-1), T given by A026758. Also T(2n+1,n+1), T given by A026747.
a(n) = T(2n-1,n-2), T given by A026758.A026763
a(n) = T(2n-1,n-2), T given by A026758.
a(n) = T(n, floor(n/2)), T given by A026758.A026764
a(n) = T(n, floor(n/2)), T given by A026758.
a(n) = Sum_{k=0..n} T(n,k), T given by A026758.A026765
a(n) = Sum_{k=0..n} T(n,k), T given by A026758.
a(n) = Sum_{k=0..floor(n/2)} T(n,k), T given by A026758.A026766
a(n) = Sum_{k=0..floor(n/2)} T(n,k), T given by A026758.
a(n) = Sum_{i=0..n} Sum_{j=0..n} T(i,j), T given by A026758.A026767
a(n) = Sum_{i=0..n} Sum_{j=0..n} T(i,j), T given by A026758.
a(n) = Sum_{k=0..floor(n/2)} T(n-k,k), T given by A026758.A026768
a(n) = Sum_{k=0..floor(n/2)} T(n-k,k), T given by A026758.
Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; T(2,1)=2; for n >= 3 and 1<=k<=n-1, T(n,k) = T(n-1,k-1) + T(n-2,k-1) + T(n-1,k) if 1<=k<=(n-1)/2, else T(n,k) = T(n-1,k-1) + T(n-1,k).A026769
Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; T(2,1)=2; for n >= 3 and 1<=k<=n-1, T(n,k) = T(n-1,k-1) + T(n-2,k-1) + T(n-1,k) if 1<=k<=(n-1)/2, else T(n,k) = T(n-1,k-1) + T(n-1,k).
a(n) = T(2n,n), T given by A026769.A026770
a(n) = T(2n,n), T given by A026769.
a(n) = T(2n,n-1), T given by A026769.A026771
a(n) = T(2n,n-1), T given by A026769.
a(n) = T(2n, n-2), T given by A026769.A026772
a(n) = T(2n, n-2), T given by A026769.
a(n) = T(2n-1,n-1), T given by A026769. Also T(2n+1,n+1), T given by A026780.A026773
a(n) = T(2n-1,n-1), T given by A026769. Also T(2n+1,n+1), T given by A026780.
a(n) = T(2n-1,n-2), T given by A026769.A026774
a(n) = T(2n-1,n-2), T given by A026769.
a(n) = T(n, floor(n/2)), T given by A026769.A026775
a(n) = T(n, floor(n/2)), T given by A026769.
a(n) = Sum_{k=0..n} T(n,k), T given by A026769.A026776
a(n) = Sum_{k=0..n} T(n,k), T given by A026769.
a(n) = Sum_{k=0..floor(n/2)} T(n,k), T given by A026769.A026777
a(n) = Sum_{k=0..floor(n/2)} T(n,k), T given by A026769.
a(n) = Sum_{i=0..n} Sum_{j=0..n} T(i,j), T given by A026769.A026778
a(n) = Sum_{i=0..n} Sum_{j=0..n} T(i,j), T given by A026769.
a(n) = Sum_{k=0..floor(n/2)} T(n-k,k), T given by A026769.A026779
a(n) = Sum_{k=0..floor(n/2)} T(n-k,k), T given by A026769.
Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; for n >= 2 and 1 <= k <= n-1, T(n,k) = T(n-1,k-1) + T(n-2,k-1) + T(n-1,k) if 1 <= k <= floor(n/2), else T(n,k) = T(n-1,k-1) + T(n-1,k).A026780
Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; for n >= 2 and 1 <= k <= n-1, T(n,k) = T(n-1,k-1) + T(n-2,k-1) + T(n-1,k) if 1 <= k <= floor(n/2), else T(n,k) = T(n-1,k-1) + T(n-1,k).
a(n) = T(2n,n), T given by A026780.A026781
a(n) = T(2n,n), T given by A026780.
a(n) = T(2n,n-1), T given by A026780.A026782
a(n) = T(2n,n-1), T given by A026780.
a(n) = T(2n, n-2), T given by A026780.A026783
a(n) = T(2n, n-2), T given by A026780.
a(n) = T(2n-1, n-1), T given by A026780.A026784
a(n) = T(2n-1, n-1), T given by A026780.
a(n) = T(2n-1, n-2), T given by A026780.A026785
a(n) = T(2n-1, n-2), T given by A026780.
a(n) = T(n, floor(n/2)), T given by A026780.A026786
a(n) = T(n, floor(n/2)), T given by A026780.
a(n) = Sum_{k=0..n} T(n,k), T given by A026780.A026787
a(n) = Sum_{k=0..n} T(n,k), T given by A026780.
a(n) = Sum_{k=0..floor(n/2)} T(n,k), T given by A026780.A026788
a(n) = Sum_{k=0..floor(n/2)} T(n,k), T given by A026780.
a(n) = Sum_{i=0..n} Sum_{j=0..n} T(i,j), T given by A026780.A026789
a(n) = Sum_{i=0..n} Sum_{j=0..n} T(i,j), T given by A026780.
a(n) = Sum_{k=0..floor(n/2)} T(n-k,k), T given by A026780.A026790
a(n) = Sum_{k=0..floor(n/2)} T(n-k,k), T given by A026780.
Triangle in which n-th row lists juxtaposed lexicographically ordered partitions of n; e.g., the partitions of 3 (1+1+1,1+2,3) appear as 1,1,1,1,2,3 in row 3.A026791
Triangle in which n-th row lists juxtaposed lexicographically ordered partitions of n; e.g., the partitions of 3 (1+1+1,1+2,3) appear as 1,1,1,1,2,3 in row 3.
List of juxtaposed reverse-lexicographically ordered partitions of the positive integers.A026792
List of juxtaposed reverse-lexicographically ordered partitions of the positive integers.
Juxtaposed partitions of 1,2,3,... into distinct parts, ordered by number of terms and then lexicographically.A026793
Juxtaposed partitions of 1,2,3,... into distinct parts, ordered by number of terms and then lexicographically.
Triangular array T read by rows: T(n,k) = number of partitions of n in which least part is k, 1<=k<=n.A026794
Triangular array T read by rows: T(n,k) = number of partitions of n in which least part is k, 1<=k<=n.
Expansion of 1/((1-2*x)*(1-6*x)*(1-9*x)*(1-10*x)).A026795
Expansion of 1/((1-2*x)*(1-6*x)*(1-9*x)*(1-10*x)).
Number of partitions of n in which the least part is 3.A026796
Number of partitions of n in which the least part is 3.
Number of partitions of n in which the least part is 4.A026797
Number of partitions of n in which the least part is 4.
Number of partitions of n in which the least part is 5.A026798
Number of partitions of n in which the least part is 5.
Number of partitions of n in which the least part is 6.A026799
Number of partitions of n in which the least part is 6.
Number of partitions of n in which the least part is 7.A026800
Number of partitions of n in which the least part is 7.
Number of partitions of n in which the least part is 8.A026801
Number of partitions of n in which the least part is 8.
Number of partitions of n in which the least part is 9.A026802
Number of partitions of n in which the least part is 9.
Number of partitions of n in which the least part is 10.A026803
Number of partitions of n in which the least part is 10.
Number of partitions of n in which the least part is odd.A026804
Number of partitions of n in which the least part is odd.
Number of partitions of n in which the least part is even.A026805
Number of partitions of n in which the least part is even.
a(n) = number of numbers k such that only one partition of n has least part k.A026806
a(n) = number of numbers k such that only one partition of n has least part k.
Triangular array T read by rows: T(n,k) = number of partitions of n in which every part is >=k, for k=1,2,...,n.A026807
Triangular array T read by rows: T(n,k) = number of partitions of n in which every part is >=k, for k=1,2,...,n.
a(n) is the number of products P of distinct positive integers satisfying P <= n.A026808
a(n) is the number of products P of distinct positive integers satisfying P <= n.
a(n) = 3^n*(3^n-1)*(3^n-2)/6.A026809
a(n) = 3^n*(3^n-1)*(3^n-2)/6.
Number of partitions of n in which the greatest part is 4.A026810
Number of partitions of n in which the greatest part is 4.