Sequences

392,541 sequences

a(n) = residue mod 2 of n-th term of A024702.A024711
a(n) = residue mod 2 of n-th term of A024702.
a(n) = residue mod 3 of n-th term of A024702.A024712
a(n) = residue mod 3 of n-th term of A024702.
a(n) = residue mod 5 of n-th term of A024702.A024713
a(n) = residue mod 5 of n-th term of A024702.
a(n) = residue mod 7 of n-th term of A024702.A024714
a(n) = residue mod 7 of n-th term of A024702.
a(n) = residue mod 11 of n-th term of A024702.A024715
a(n) = residue mod 11 of n-th term of A024702.
a(n) = Sum_{1 <= j <= i <= n} S(i,j), where S(i,j) are Stirling numbers of the second kind.A024716
a(n) = Sum_{1 <= j <= i <= n} S(i,j), where S(i,j) are Stirling numbers of the second kind.
Sum of max{S(i,j): 1<=j<=i} for i = 1,2,...,n, where S(i,j) are Stirling numbers of the second kind.A024717
Sum of max{S(i,j): 1<=j<=i} for i = 1,2,...,n, where S(i,j) are Stirling numbers of the second kind.
a(n) = (1/2)*(1 + Sum_{k=0..n} binomial(2*k, k)).A024718
a(n) = (1/2)*(1 + Sum_{k=0..n} binomial(2*k, k)).
a(n) = (1/3)*(2 + Sum_{k=0..n} C(3k,k)).A024719
a(n) = (1/3)*(2 + Sum_{k=0..n} C(3k,k)).
a(n) = (1/4)*(3 + Sum_{k=0..n} C(4k,k)).A024720
a(n) = (1/4)*(3 + Sum_{k=0..n} C(4k,k)).
a(n) = (1/5)*(4 + Sum_{k=0..n} C(5*k,k)).A024721
a(n) = (1/5)*(4 + Sum_{k=0..n} C(5*k,k)).
a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=a(2)=1.A024722
a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=a(2)=1.
a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=a(2)=1 and a(3)=2.A024723
a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=a(2)=1 and a(3)=2.
A024723(n+3)/2.A024724
A024723(n+3)/2.
a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=a(2)=1 and a(3)=3.A024725
a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=a(2)=1 and a(3)=3.
a(n) = s(n+3)/3, where s(n) = A024725(n).A024726
a(n) = s(n+3)/3, where s(n) = A024725(n).
a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=a(2)=1 and a(3)=4.A024727
a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=a(2)=1 and a(3)=4.
a(n) = A024727(n+3)/4.A024728
a(n) = A024727(n+3)/4.
a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=a(2)=1 and a(3)=5.A024729
a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=a(2)=1 and a(3)=5.
a(n) = s(n+3)/5, where s is A024729.A024730
a(n) = s(n+3)/5, where s is A024729.
a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=a(2)=1 and a(3)=6.A024731
a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=a(2)=1 and a(3)=6.
a(n) = s(n+3)/6, where s is A024731.A024732
a(n) = s(n+3)/6, where s is A024731.
a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=a(2)=1 and a(3)=7.A024733
a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=a(2)=1 and a(3)=7.
a(n) = A024733(n+3)/7.A024734
a(n) = A024733(n+3)/7.
a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=2 and a(2)=a(3)=1.A024735
a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=2 and a(2)=a(3)=1.
s(n+3)/2, where s is A024735.A024736
s(n+3)/2, where s is A024735.
a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=3 and a(2)=a(3)=1.A024737
a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=3 and a(2)=a(3)=1.
a(n) = s(n+3)/3, where s is A024737.A024738
a(n) = s(n+3)/3, where s is A024737.
a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=a(3)=2 and a(2)=1.A024739
a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=a(3)=2 and a(2)=1.
s(n+3)/4, where s is A024739.A024740
s(n+3)/4, where s is A024739.
a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=2, a(2)=1, and a(3)=3.A024741
a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=2, a(2)=1, and a(3)=3.
a(n) = A024741(n+3)/6.A024742
a(n) = A024741(n+3)/6.
a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=3, a(2)=1, and a(3)=2.A024743
a(n) = Sum_{i=1..floor((n+1)/4)} a(2*i-1) * a(n-2*i+1), with a(1)=3, a(2)=1, and a(3)=2.
a(n) = s(n+3)/6, where s is A024743.A024744
a(n) = s(n+3)/6, where s is A024743.
Binomial coefficients: C(n,k), 1 <= k <= n-1, sorted.A024745
Binomial coefficients: C(n,k), 1 <= k <= n-1, sorted.
Binomial coefficients: C(n,k), 2 <= k <= n-2, sorted.A024746
Binomial coefficients: C(n,k), 2 <= k <= n-2, sorted.
Binomial coefficients: C(n,k), 3 <= k <= n-3, sorted.A024747
Binomial coefficients: C(n,k), 3 <= k <= n-3, sorted.
Binomial coefficients: C(n,k), 4 <= k <= n-4, sorted.A024748
Binomial coefficients: C(n,k), 4 <= k <= n-4, sorted.
Binomial coefficients: C(n,k), 5 <= k <= n-5, sorted.A024749
Binomial coefficients: C(n,k), 5 <= k <= n-5, sorted.
Binomial coefficients: C(n,k), 6 <= k <= n-6, sorted.A024750
Binomial coefficients: C(n,k), 6 <= k <= n-6, sorted.
Binomial coefficients: C(n,k), 7 <= k <= n-7, sorted.A024751
Binomial coefficients: C(n,k), 7 <= k <= n-7, sorted.
Binomial coefficients: C(n,k), 8 <= k <= n-8, sorted.A024752
Binomial coefficients: C(n,k), 8 <= k <= n-8, sorted.
Binomial coefficients: C(n,k), 9 <= k <= n-9, sorted.A024753
Binomial coefficients: C(n,k), 9 <= k <= n-9, sorted.
Binomial coefficients: C(n,k), 10 <= k <= n-10, sorted.A024754
Binomial coefficients: C(n,k), 10 <= k <= n-10, sorted.
Binomial coefficients: C(n,k), 3 <= k <= n-3, sorted, duplicates removed.A024755
Binomial coefficients: C(n,k), 3 <= k <= n-3, sorted, duplicates removed.
Binomial coefficients: C(n,k), 4 <= k <= n-4, sorted, duplicates removed.A024756
Binomial coefficients: C(n,k), 4 <= k <= n-4, sorted, duplicates removed.
Binomial coefficients: C(n,k), 5 <= k <= n-5, sorted, duplicates removed.A024757
Binomial coefficients: C(n,k), 5 <= k <= n-5, sorted, duplicates removed.
Binomial coefficients: C(n,k), 6 <= k <= n-6, sorted, duplicates removed.A024758
Binomial coefficients: C(n,k), 6 <= k <= n-6, sorted, duplicates removed.
Binomial coefficients: C(n,k), 7 <= k <= n-7, sorted, duplicates removed.A024759
Binomial coefficients: C(n,k), 7 <= k <= n-7, sorted, duplicates removed.
Binomial coefficients: C(n,k), 8 <= k <= n-8, sorted, duplicates removed.A024760
Binomial coefficients: C(n,k), 8 <= k <= n-8, sorted, duplicates removed.