A336091 Number of ordered ways of writing the n-th n-gonal pyramidal number as a sum of n n-gonal pyramidal numbers (with 0's allowed).

1, 1, 2, 3, 10, 5, 246, 1519, 19678, 74601, 690490, 21026621, 301528272, 4397123315, 71221546592, 1001245733295, 19276579678736, 368677642975493, 6820451221691646, 136000924000323691, 3069656935024721420, 69646109074231173897, 1641880679174919030100

Offset: 0

Author

Ilya Gutkovskiy, Oct 04 2020

Keywords

• nonn

Examples

			a(3) = 3 because the third tetrahedral (or triangular pyramidal) number is 10 and we have [10, 0, 0], [0, 10, 0] and [0, 0, 10].
		

Links

• Eric Weisstein's World of Mathematics, Pyramidal Number
• Index to sequences related to pyramidal numbers

Crossrefs

Cf. A006484, A196010, A335633, A336303, A337797, A337798, A337799.

Programs

Mathematica

Table[SeriesCoefficient[Sum[x^(k (k + 1) (k (n - 2) - n + 5)/6), {k, 0, n}]^n, {x, 0, n (n + 1) (n^2 - 3 n + 5)/6}], {n, 0, 22}]

Formula

a(n) = [x^p(n,n)] (Sum_{k=0..n} x^p(n,k))^n, where p(n,k) = k * (k + 1) * (k * (n - 2) - n + 5) / 6 is the k-th n-gonal pyramidal number.