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%I #9 May 31 2022 02:39:43
%S 1,1,6,31,211,1841,18547,210664,2682657,37807531,581985596,9696297528,
%T 173702897000,3327063115248,67790086866271,1462900566163696,
%U 33310115601839624,797687851718024035,20032231443590167914,526189230537615409571,14423255501358439152231
%N G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - x)^5) / (1 - x)^5.
%H Seiichi Manyama, <a href="/A351818/b351818.txt">Table of n, a(n) for n = 0..452</a>
%F a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n+4*k+3,n-k-1) * a(k).
%t nmax = 20; A[_] = 0; Do[A[x_] = 1 + x A[x/(1 - x)^5]/(1 - x)^5 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t a[0] = 1; a[n_] := a[n] = Sum[Binomial[n + 4 k + 3, n - k - 1] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 20}]
%Y Cf. A000110, A045500, A125274, A351815, A351816, A351817.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Feb 20 2022