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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 02 2021
STATUS
approved