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 A337001 #17 Jan 13 2024 06:46:30
%S A337001 0,1,10,57,292,1585,9726,68425,547912,4931937,49320370,542525401,
%T A337001 6510306540,84633987217,1184875823782,17773137360105,284370197765776,
%U A337001 4834293362023105,87017280516421722,1653328329812019577,33066566596240399540,694397898521048399601
%N A337001 a(n) = n! * Sum_{k=0..n} k^3 / k!.
%C A337001 Exponential convolution of cubes (A000578) and factorial numbers (A000142).
%H A337001 Seiichi Manyama, <a href="/A337001/b337001.txt">Table of n, a(n) for n = 0..449</a>
%F A337001 E.g.f.: x * (1 + 3*x + x^2) * exp(x) / (1 - x).
%F A337001 a(0) = 0; a(n) = n * (n^2 + a(n-1)).
%F A337001 a(n) ~ 5*exp(1)*n!. - _Vaclav Kotesovec_, Jan 13 2024
%t A337001 Table[n! Sum[k^3/k!, {k, 0, n}], {n, 0, 21}]
%t A337001 nmax = 21; CoefficientList[Series[x (1 + 3 x + x^2) Exp[x]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!
%t A337001 a[0] = 0; a[n_] := a[n] = n (n^2 + a[n - 1]); Table[a[n], {n, 0, 21}]
%o A337001 (PARI) a(n) = n! * sum(k=0, n, k^3/k!); \\ _Michel Marcus_, Aug 12 2020
%Y A337001 Cf. A000142, A000522, A000578, A007526, A030297, A256016, A337002.
%Y A337001 Row sums of A121682.
%K A337001 nonn
%O A337001 0,3
%A A337001 _Ilya Gutkovskiy_, Aug 10 2020