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%I #10 Aug 07 2023 08:31:26
%S 1,1,2,9,53,386,3422,35300,412084,5364255,76952267,1203835714,
%T 20362911276,369906504888,7175947738672,147944905766929,
%U 3227970924123268,74264452788294013,1795825803391367571,45514495928632484735,1205981001167335524448,33331235326744168532151
%N G.f. A(x) satisfies A(x) = 1 + x * A(x/(1 - x)^5) / (1 - x).
%H Seiichi Manyama, <a href="/A351815/b351815.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-1,n-k-1) * a(k).
%t nmax = 21; A[_] = 0; Do[A[x_] = 1 + x A[x/(1 - x)^5]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t a[0] = 1; a[n_] := a[n] = Sum[Binomial[n + 4 k - 1, n - k - 1] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 21}]
%Y Cf. A000110, A125273, A351813, A351814.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Feb 20 2022