A374892 Obverse convolution (n)**(n(n+1)/2); see Comments.

0, 1, 12, 216, 5600, 198000, 9144576, 533653120, 38339288064, 3320915760000, 340950896000000, 40905397939101696, 5666507699182387200, 897094997540641908736, 160875919414586880000000, 32426573960663769600000000, 7296186062362650316241371136

Offset: 0

Author

Clark Kimberling, Sep 14 2024

Keywords

• nonn

Comments

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

Crossrefs

Cf. A000027, A000217, A374848.

Programs

Mathematica

s[n_] := n; t[n_] := n (n + 1)/2;
u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
Table[u[n], {n, 0, 20}]

Formula

a(n) ~ n^(2*n+1) / (2^n * exp(2*n + 2 - Pi*sqrt(2*n))). - Vaclav Kotesovec, Sep 15 2024