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%I #11 Aug 02 2021 15:51:32
%S 1,1,8,92,1289,20518,358611,6749268,135095116,2851394415,63066764910,
%T 1454808403309,34869538474423,865771965143262,22211885496614803,
%U 587583912259110350,15998031596388750905,447598845624472993496,12850922242548662924046,378153449033278630907275
%N a(n) = Sum_{k=0..n} Stirling2(n,k) * binomial(7*k,k) / (6*k + 1).
%C Stirling transform of A002296.
%H Michael De Vlieger, <a href="/A346768/b346768.txt">Table of n, a(n) for n = 0..493</a>
%F G.f.: Sum_{k>=0} ( binomial(7*k,k) / (6*k + 1) ) * x^k / Product_{j=0..k} (1 - j*x).
%t Table[Sum[StirlingS2[n, k] Binomial[7 k, k]/(6 k + 1), {k, 0, n}], {n, 0, 19}]
%t 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]
%t 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]!
%o (PARI) a(n) = sum(k=0, n, stirling(n, k, 2)*binomial(7*k, k)/(6*k + 1)); \\ _Michel Marcus_, Aug 02 2021
%Y Cf. A002296, A064856, A346764, A346765, A346766, A346767, A346769.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Aug 02 2021