7567560

Appears in sequences

• E.g.f.: (1 + 15*x + (45/2)*x^2 + (5/2)*x^3)/(1 - 2*x)^(13/2).at n=5A038121
• This table shows the coefficients of combinatorial formulas needed for generating the sequential sums of p-th powers of binomial coefficients C(n,5). The p-th row (p>=1) contains a(i,p) for i=1 to 5*p-4, where a(i,p) satisfies Sum_{i=1..n} C(i+4,5)^p = 6 * C(n+5,6) * Sum_{i=1..5*p-4} a(i,p) * C(n-1,i-1)/(i+5).at n=32A087109
• Least common multiple of all cycle sizes in range [A014137(n-1)..A014138(n-1)] of permutation A071661/A071662.at n=10A089403
• Triangle read by rows: row n gives number of matchings of size 0<=k<=n (edges) in the complete graph on 2*n >= 2 vertices.at n=40A119743
• Number of cycles with entries of the same parity in all fixed-point-free involutions of {1,2,...,2n}.at n=8A161122
• Exponential Riordan array [1/sqrt(1-2x), x/(1-2x)].at n=39A176230
• A Galton triangle: T(n,k) = 2*k*T(n-1,k) + (2*k-1)*T(n-1,k-1).at n=34A187075
• Triangle T(n,k), 0<=k<=n, given by (0,2,0,4,0,6,0,8,0,10,0,...) DELTA (1, 2, 3, 4, 5, 6, 7, 8, 9,...) where DELTA is the operator defined in A084938.at n=43A211402
• Triangle read by rows in which the n-th row lists the multinomials A036038 for all partitions of 2n with only even parts in Abramowitz-Stegun ordering.at n=40A257468
• Triangle read by rows, T(n,k) = C(2*n,n+k)*Sum_{m=0..k} (-1)^(m+k)*C(n+k,n+m)* Stirling1(n+m,m), for n>=0 and 0<=k<=n.at n=34A268440
• Number of set partitions of [n] with minimal block length multiplicity equal to five.at n=11A271765
• Coefficient triangle of generalized Laguerre polynomials n!*L(n,n+1,x) (rising powers of x).at n=30A343890
• Diagonal of rational function 1/(1 - (x^3 + y^3 + z^3 + x^4*y*z)).at n=17A361739
• Numbers that occur exactly 5 times in A036038, i.e., numbers m such that the multinomial coefficient (x_1 + ... + x_k)!/(x_1! * ... * x_k!) is equal to m for exactly 5 integer partitions (x_1, ..., x_k).at n=14A376375