OFFSET
0,3
COMMENTS
See A374848 for the definition of obverse convolution and a guide to related sequences. a(2k+1) is a square for k>=0.
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
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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jul 31 2024
STATUS
approved