OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Polygonal Number
FORMULA
a(n) = [x^p(n,n)] (Sum_{k=0..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(3) = 6 because the third triangular number is 6 and we have [6, 0, 0], [0, 6, 0], [0, 0, 6], [3, 3, 0], [3, 0, 3] and [0, 3, 3].
MATHEMATICA
Table[SeriesCoefficient[Sum[x^(k (k (n - 2) - n + 4)/2), {k, 0, n}]^n, {x, 0, n (n^2 - 3 n + 4)/2}], {n, 0, 23}]
PROG
(PARI)
p(n, k) = {k * (k * (n - 2) - n + 4) / 2}
a(n) = {my(m=p(n, n)); polcoef((sum(k=0, 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