A374885 Obverse convolution (n^2)**(n(n+1)/2); see Comments.

0, 1, 24, 1080, 78400, 8415000, 1254839040, 248351295808, 63008824320000, 19941885512640000, 7702879929184000000, 3566623957287040742400, 1950112829958404302503936, 1243182598706645953527808000, 913988528405739663528960000000

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. A000217, A000290, A374848.

Programs

Mathematica

s[n_] := n^2; 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+2) / (2^((n+2)/3) * exp(2*n - (2*n+1)*Pi/(3*sqrt(2)))). - Vaclav Kotesovec, Jul 31 2024