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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 02 2021
STATUS
approved