A346768 a(n) = Sum_{k=0..n} Stirling2(n,k) * binomial(7*k,k) / (6*k + 1).

1, 1, 8, 92, 1289, 20518, 358611, 6749268, 135095116, 2851394415, 63066764910, 1454808403309, 34869538474423, 865771965143262, 22211885496614803, 587583912259110350, 15998031596388750905, 447598845624472993496, 12850922242548662924046, 378153449033278630907275

Offset: 0

Author

Ilya Gutkovskiy, Aug 02 2021

Keywords

• nonn

Comments

Stirling transform of A002296.

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..493

Crossrefs

Cf. A002296, A064856, A346764, A346765, A346766, A346767, A346769.

Programs

Mathematica

Table[Sum[StirlingS2[n, k] Binomial[7 k, k]/(6 k + 1), {k, 0, n}], {n, 0, 19}]
nmax = 19; CoefficientList[Series[Sum[(Binomial[7 k, k]/(6 k + 1)) x^k/Product[1 - j x, {j, 0, k}], {k, 0, nmax}], {x, 0, nmax}], x]
nmax = 19; CoefficientList[Series[HypergeometricPFQ[{1/7, 2/7, 3/7, 4/7, 5/7, 6/7}, {1/3, 1/2, 2/3, 5/6,1, 7/6}, 823543 (Exp[x] - 1)/46656], {x, 0, nmax}], x] Range[0, nmax]!

PARI

a(n) = sum(k=0, n, stirling(n, k, 2)*binomial(7*k, k)/(6*k + 1)); \\ Michel Marcus, Aug 02 2021

Formula

G.f.: Sum_{k>=0} ( binomial(7*k,k) / (6*k + 1) ) * x^k / Product_{j=0..k} (1 - j*x).