OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Pyramidal Number
FORMULA
a(n) = [x^p(n,n)] 1 / (1 - Sum_{k=1..n} x^p(n,k)), where p(n,k) = k * (k + 1) * (k * (n - 2) - n + 5) / 6 is the k-th n-gonal pyramidal number.
EXAMPLE
a(3) = 15 because the third tetrahedral (or triangular pyramidal) number is 10 and we have [10], [4, 4, 1, 1], [4, 1, 4, 1], [4, 1, 1, 4], [1, 4, 4, 1], [1, 4, 1, 4], [1, 1, 4, 4], [4, 1, 1, 1, 1, 1, 1], [1, 4, 1, 1, 1, 1, 1], [1, 1, 4, 1, 1, 1, 1], [1, 1, 1, 4, 1, 1, 1], [1, 1, 1, 1, 4, 1, 1], [1, 1, 1, 1, 1, 4, 1], [1, 1, 1, 1, 1, 1, 4] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1].
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 22 2020
STATUS
approved