A337797 Number of partitions of the n-th n-gonal pyramidal number into n-gonal pyramidal numbers.

1, 1, 2, 4, 13, 45, 198, 858, 3728, 16115, 69125, 292940, 1224628, 5052396, 20570806, 82655098, 327881398, 1284663878, 4973614490, 19034194696, 72037124003, 269723590850, 999517370314, 3667158097572, 13325691939021, 47975192145998

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Eric Weisstein's World of Mathematics, Pyramidal Number

Index entries for sequences related to partitions

Index to sequences related to pyramidal numbers

Formula

a(n) = [x^p(n,n)] Product_{k=1..n} 1 / (1 - 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) = 4 because the third tetrahedral (or triangular pyramidal) number is 10 and we have [10], [4, 4, 1, 1], [4, 1, 1, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1].

Crossrefs

Cf. A006484, A072964, A298269, A337762, A337798, A337799.

Sequence in context: A193057 A115600 A007858 * A300931 A286074 A153930

Adjacent sequences: A337794 A337795 A337796 * A337798 A337799 A337800

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 22 2020

Status

approved