OFFSET
0,6
LINKS
Eric Weisstein's World of Mathematics, Polygonal Number
FORMULA
a(n) = [x^p(n,n)] (Sum_{k=1..n} x^p(n,k))^n, where p(n,k) = k * (k * (n - 2) - n + 4) / 2 is the k-th n-gonal number.
EXAMPLE
a(4) = 1 because the fourth square is 16 and we have [4, 4, 4, 4].
MATHEMATICA
Join[{1}, Table[SeriesCoefficient[Sum[x^(k (k (n - 2) - n + 4)/2), {k, 1, n}]^n, {x, 0, n (n^2 - 3 n + 4)/2}], {n, 1, 24}]]
PROG
(PARI)
p(n, k) = {k * (k * (n - 2) - n + 4) / 2}
a(n) = {my(m=p(n, n)); polcoef((sum(k=1, n, x^p(n, k)) + O(x*x^m))^n, m)} \\ Andrew Howroyd, Oct 03 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 03 2020
STATUS
approved