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A375050
Obverse convolution (n(n+1)/2)**(n(n+1)/2); see Comments.
2
0, 1, 18, 576, 29400, 2205225, 228953088, 31473598464, 5537223659520, 1213834310015625, 324468643299372000, 103900389446258786304, 39267840204934404964992, 17296280109081832136303025, 8783270052027947513856000000, 5094007565002120817604034560000
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
Sequence in context: A183498 A254381 A177098 * A133401 A211708 A341305
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jul 31 2024
STATUS
approved