A375050 Obverse convolution (n(n+1)/2)**(n(n+1)/2); see Comments.

0, 1, 18, 576, 29400, 2205225, 228953088, 31473598464, 5537223659520, 1213834310015625, 324468643299372000, 103900389446258786304, 39267840204934404964992, 17296280109081832136303025, 8783270052027947513856000000, 5094007565002120817604034560000

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. a(2k+1) is a square for k>=0.

Crossrefs

Cf. A000217, A374848.

Programs

Maple

t:= n-> n*(n+1)/2:
a:= n-> mul(t(n-j)+t(j), j=0..n):
seq(a(n), n=0..15);  # Alois P. Heinz, Aug 02 2024

Mathematica

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

Formula

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

a(n) = (n*(n+1)/2) * [1-(n+s)/2]n * [1-(n-s)/2]_n, where s = sqrt(-n*(2 + n)) and [x]_n is the Pochhammer function. - _Peter Luschny, Aug 02 2024