OFFSET
0,3
COMMENTS
Stirling transform of A002296.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..493
FORMULA
G.f.: Sum_{k>=0} ( binomial(7*k,k) / (6*k + 1) ) * x^k / Product_{j=0..k} (1 - j*x).
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]!
PROG
(PARI) a(n) = sum(k=0, n, stirling(n, k, 2)*binomial(7*k, k)/(6*k + 1)); \\ Michel Marcus, Aug 02 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 02 2021
STATUS
approved