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A346769
a(n) = Sum_{k=0..n} Stirling2(n,k) * binomial(8*k,k) / (7*k + 1).
6
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
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 02 2021
STATUS
approved