OFFSET
0,3
LINKS
David A. Corneth, Table of n, a(n) for n = 0..278 (first 51 terms from Vaclav Kotesovec)
Eric Weisstein's World of Mathematics, Polygonal Number
FORMULA
a(n) = [x^p(n,n)] Product_{k=1..n} 1 / (1 - x^p(n,k)), where p(n,k) = k * (k * (n - 2) - n + 4) / 2 is the k-th n-gonal number.
EXAMPLE
a(3) = 4 because the third triangular number is 6 and we have [6], [3, 3], [3, 1, 1, 1] and [1, 1, 1, 1, 1, 1].
MATHEMATICA
nmax = 20; Table[SeriesCoefficient[Product[1/(1 - x^(k*((k*(n - 2) - n + 4)/2))), {k, 1, n}], {x, 0, n*(4 - 3*n + n^2)/2}], {n, 0, nmax}] (* Vaclav Kotesovec, Sep 19 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 19 2020
STATUS
approved