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

0,3

Links

Table of n, a(n) for n=0..22.

Eric Weisstein's World of Mathematics, Pyramidal Number

Index to sequences related to pyramidal numbers

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.

Example

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].

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}]

Crossrefs

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

Sequence in context: A292239 A163767 A343936 * A347835 A128531 A123167

Adjacent sequences: A336088 A336089 A336090 * A336092 A336093 A336094

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 04 2020

Status

approved