A336303 Number of ordered ways of writing the n-th n-gonal pyramidal number as a sum of n nonzero n-gonal pyramidal numbers.

1, 1, 0, 0, 6, 0, 180, 630, 1120, 36288, 441000, 6579870, 59734620, 1252872192, 13668490836, 162131872695, 2971275208720, 52783774330940, 1334562954639156, 16933262255752698, 406499325562503480, 8838644883526856832, 190698441426122689290

Offset

0,5

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=1..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(4) = 6 because the fourth square pyramidal number is 30 and we have [14, 14, 1, 1], [14, 1, 14, 1], [14, 1, 1, 14], [1, 14, 14, 1], [1, 14, 1, 14] and [1, 1, 14, 14].

Mathematica

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

Crossrefs

Cf. A006484, A298858, A335634, A336091, A337797, A337798, A337799.

Sequence in context: A240818 A134680 A362794 * A111372 A294686 A179936

Adjacent sequences: A336300 A336301 A336302 * A336304 A336305 A336306

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 04 2020

Status

approved