This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A376097 #7 Sep 10 2024 04:09:20
%S A376097 1,1,17,1410,364019,228282823,296324235500,712075198644414,
%T A376097 2918094100584013255,19151474626728425949663,
%U A376097 191553141880332262049655201,2804913258838830873001491036584,58168297154586087400230338311689652,1661461159115675581245556180230933084340
%N A376097 a(0) = 1; a(n) = Sum_{k=0..n-1} (k+1)^4 * a(k) * a(n-k-1).
%F A376097 G.f. A(x) satisfies: A(x) = 1 + x * A(x)^2 + 15 * x^2 * A(x) * A'(x) + 25 * x^3 * A(x) * A''(x) + 10 * x^4 * A(x) * A'''(x) + x^5 * A(x) * A''''(x).
%t A376097 a[0] = 1; a[n_] := a[n] = Sum[(k + 1)^4 a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 13}]
%t A376097 nmax = 13; A[_] = 0; Do[A[x_] = 1 + x A[x]^2 + 15 x^2 A[x] A'[x] + 25 x^3 A[x] A''[x] + 10 x^4 A[x] A'''[x] + x^5 A[x] A''''[x] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%Y A376097 Cf. A000699, A015085, A088716, A256020, A376095, A376096.
%K A376097 nonn
%O A376097 0,3
%A A376097 _Ilya Gutkovskiy_, Sep 10 2024