A374881 Obverse convolution (n)**(n^2); see Comments.

0, 1, 16, 405, 15360, 818125, 58226688, 5332085577, 610140160000, 85235284359225, 14264819712000000, 2815701027697558429, 646960843646287478784, 171112492588968115453125, 51595090958399913852928000, 17587698619968027952119140625

Offset: 0

Author

Clark Kimberling, Jul 31 2024

Keywords

• nonn

Comments

See A374848 for the definition of obverse convolution and a guide to related sequences.

Crossrefs

Cf. A000027, A000290, A374848, A376523, A376524.

Programs

Mathematica

s[n_] := n; t[n_] := n^2;
u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
Table[u[n], {n, 0, 18}]

Formula

a(n) ~ n^(2*n + 1) / exp(2*n + 1 - Pi*sqrt(n)). - Vaclav Kotesovec, Jul 31 2024