A337763 Number of partitions of the n-th n-gonal number into distinct n-gonal numbers.

1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 4, 4, 2, 2, 4, 7, 8, 5, 6, 14, 6, 13, 23, 16, 19, 32, 34, 48, 56, 62, 73, 137, 126, 203, 257, 256, 409, 503, 612, 794, 1097, 1203, 1737, 2141, 2773, 3322, 4527, 5087, 7497, 8214, 11238, 12598

Offset

0,6

Links

Table of n, a(n) for n=0..54.

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 + x^p(n,k)), where p(n,k) = k * (k * (n - 2) - n + 4) / 2 is the k-th n-gonal number.

Example

a(5) = 2 because 5th pentagonal number is 35 and we have [35] and [22, 12, 1].

Crossrefs

Cf. A000009, A030273, A060354, A288126, A337762, A337764.

Sequence in context: A274888 A239702 A202084 * A109072 A100727 A366134

Adjacent sequences: A337760 A337761 A337762 * A337764 A337765 A337766

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 19 2020

Status

approved