A346765 a(n) = Sum_{k=0..n} Stirling2(n,k) * binomial(4*k,k) / (3*k + 1).

1, 1, 5, 35, 301, 2980, 32824, 394119, 5089387, 70008606, 1018551386, 15586572831, 249761256325, 4175639393112, 72613795311014, 1310044170067051, 24465311302401475, 472024733580022982, 9392470260695334398, 192455730876780393835, 4055291189439769281557

Offset

0,3

Comments

Stirling transform of A002293.

Links

Michael De Vlieger, Table of n, a(n) for n = 0..514

Formula

G.f.: Sum_{k>=0} ( binomial(4*k,k) / (3*k + 1) ) * x^k / Product_{j=0..k} (1 - j*x).

Mathematica

Table[Sum[StirlingS2[n, k] Binomial[4 k, k]/(3 k + 1), {k, 0, n}], {n, 0, 20}]
nmax = 20; CoefficientList[Series[Sum[(Binomial[4 k, k]/(3 k + 1)) x^k/Product[1 - j x, {j, 0, k}], {k, 0, nmax}], {x, 0, nmax}], x]
nmax = 20; CoefficientList[Series[HypergeometricPFQ[{1/4, 1/2, 3/4}, {2/3, 1, 4/3}, 256 (Exp[x] - 1)/27], {x, 0, nmax}], x] Range[0, nmax]!

Prog

(PARI) a(n) = sum(k=0, n, stirling(n, k, 2)*binomial(4*k, k)/(3*k + 1)); \\ Michel Marcus, Aug 02 2021

Crossrefs

Cf. A002293, A064856, A346764, A346766, A346767, A346768, A346769.

Sequence in context: A370844 A027392 A291813 * A177354 A253096 A305964

Adjacent sequences: A346762 A346763 A346764 * A346766 A346767 A346768

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 02 2021

Status

approved