A346766 a(n) = Sum_{k=0..n} Stirling2(n,k) * binomial(5*k,k) / (4*k + 1).

1, 1, 6, 51, 531, 6331, 83532, 1195452, 18316582, 297727712, 5099398853, 91554269703, 1715910362408, 33457504204403, 676778172939139, 14168046060375184, 306327815585165519, 6827996259530724139, 156654003923243040925, 3694188118839057258940, 89428870506038692255920

Offset

0,3

Comments

Stirling transform of A002294.

Links

Table of n, a(n) for n=0..20.

Formula

G.f.: Sum_{k>=0} ( binomial(5*k,k) / (4*k + 1) ) * x^k / Product_{j=0..k} (1 - j*x).

Mathematica

Table[Sum[StirlingS2[n, k] Binomial[5 k, k]/(4 k + 1), {k, 0, n}], {n, 0, 20}]
nmax = 20; CoefficientList[Series[Sum[(Binomial[5 k, k]/(4 k + 1)) x^k/Product[1 - j x, {j, 0, k}], {k, 0, nmax}], {x, 0, nmax}], x]
nmax = 20; CoefficientList[Series[HypergeometricPFQ[{1/5, 2/5, 3/5, 4/5}, {1/2, 3/4, 1, 5/4}, 3125 (Exp[x] - 1)/256], {x, 0, nmax}], x] Range[0, nmax]!

Prog

(PARI) a(n) = sum(k=0, n, stirling(n, k, 2)*binomial(5*k, k)/(4*k + 1)); \\ Michel Marcus, Aug 03 2021

Crossrefs

Cf. A002294, A064856, A346764, A346765, A346767, A346768, A346769.

Sequence in context: A215159 A263895 A027393 * A305965 A255518 A208250

Adjacent sequences: A346763 A346764 A346765 * A346767 A346768 A346769

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 02 2021

Status

approved