A337762 Number of partitions of the n-th n-gonal number into n-gonal numbers.

1, 1, 2, 4, 8, 21, 56, 144, 370, 926, 2275, 5482, 12966, 30124, 68838, 154934, 343756, 752689, 1627701, 3479226, 7355608, 15390682, 31889732, 65465473, 133212912, 268811363, 538119723, 1069051243, 2108416588, 4129355331, 8033439333

Offset

0,3

Links

David A. Corneth, Table of n, a(n) for n = 0..278 (first 51 terms from Vaclav Kotesovec)

Eric Weisstein's World of Mathematics, Polygonal Number

Index entries for sequences related to partitions

Index to sequences related to polygonal numbers

Formula

a(n) = [x^p(n,n)] Product_{k=1..n} 1 / (1 - x^p(n,k)), where p(n,k) = k * (k * (n - 2) - n + 4) / 2 is the k-th n-gonal number.

Example

a(3) = 4 because the third triangular number is 6 and we have [6], [3, 3], [3, 1, 1, 1] and [1, 1, 1, 1, 1, 1].

Mathematica

nmax = 20; Table[SeriesCoefficient[Product[1/(1 - x^(k*((k*(n - 2) - n + 4)/2))), {k, 1, n}], {x, 0, n*(4 - 3*n + n^2)/2}], {n, 0, nmax}] (* Vaclav Kotesovec, Sep 19 2020 *)

Crossrefs

Cf. A000041, A037444, A060354, A072964, A337763, A337764.

Sequence in context: A002040 A162110 A108071 * A055876 A065847 A133604

Adjacent sequences: A337759 A337760 A337761 * A337763 A337764 A337765

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 19 2020

Status

approved