A346764 a(n) = Sum_{k=0..n} Stirling2(n,k) * binomial(3*k,k) / (2*k + 1).

1, 1, 4, 22, 149, 1169, 10272, 99012, 1032346, 11526094, 136755650, 1714031312, 22584475206, 311597054110, 4486616619986, 67227958200996, 1045724188868353, 16849477086762701, 280694278424099214, 4826423610068933738, 85527389275821664161, 1559842051063534891301

Offset

0,3

Comments

Stirling transform of A001764.

Links

Michael De Vlieger, Table of n, a(n) for n = 0..525

Formula

G.f.: Sum_{k>=0} ( binomial(3*k,k) / (2*k + 1) ) * x^k / Product_{j=0..k} (1 - j*x).

Mathematica

Table[Sum[StirlingS2[n, k] Binomial[3 k, k]/(2 k + 1), {k, 0, n}], {n, 0, 21}]
nmax = 21; CoefficientList[Series[Sum[(Binomial[3 k, k]/(2 k + 1)) x^k/Product[1 - j x, {j, 0, k}], {k, 0, nmax}], {x, 0, nmax}], x]
nmax = 21; CoefficientList[Series[HypergeometricPFQ[{1/3, 2/3}, {1, 3/2}, 27 (Exp[x] - 1)/4], {x, 0, nmax}], x] Range[0, nmax]!

Prog

(PARI) a(n) = sum(k=0, n, stirling(n, k, 2)*binomial(3*k, k)/(2*k + 1)); \\ Michel Marcus, Aug 02 2021

Crossrefs

Cf. A001764, A064856, A346765, A346766, A346767, A346768, A346769.

Sequence in context: A368733 A253095 A111529 * A228883 A307439 A189845

Adjacent sequences: A346761 A346762 A346763 * A346765 A346766 A346767

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 02 2021

Status

approved