A346769 a(n) = Sum_{k=0..n} Stirling2(n,k) * binomial(8*k,k) / (7*k + 1).

1, 1, 9, 117, 1849, 33099, 648683, 13652529, 304828941, 7160371928, 175882500852, 4497024667232, 119255943612372, 3270580645588057, 92537409967439493, 2695752129992788115, 80716475549045336327, 2480352681613911495046, 78120174740199126232258

Offset

0,3

Comments

Stirling transform of A007556.

Links

Michael De Vlieger, Table of n, a(n) for n = 0..488

Formula

G.f.: Sum_{k>=0} ( binomial(8*k,k) / (7*k + 1) ) * x^k / Product_{j=0..k} (1 - j*x).

Mathematica

Table[Sum[StirlingS2[n, k] Binomial[8 k, k]/(7 k + 1), {k, 0, n}], {n, 0, 18}]
nmax = 18; CoefficientList[Series[Sum[(Binomial[8 k, k]/(7 k + 1)) x^k/Product[1 - j x, {j, 0, k}], {k, 0, nmax}], {x, 0, nmax}], x]
nmax = 18; CoefficientList[Series[HypergeometricPFQ[{1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8}, {2/7, 3/7, 4/7, 5/7, 6/7, 1, 8/7}, 16777216 (Exp[x] - 1)/823543], {x, 0, nmax}], x] Range[0, nmax]!

Prog

(PARI) a(n) = sum(k=0, n, stirling(n, k, 2)*binomial(8*k, k)/(7*k + 1)); \\ Michel Marcus, Aug 02 2021

Crossrefs

Cf. A007556, A064856, A346764, A346765, A346766, A346767, A346768.

Sequence in context: A180904 A062994 A059967 * A304184 A255521 A027396

Adjacent sequences: A346766 A346767 A346768 * A346770 A346771 A346772

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 02 2021

Status

approved