A337764 Number of compositions (ordered partitions) of the n-th n-gonal number into n-gonal numbers.

1, 1, 2, 7, 124, 14371, 12842911, 103590035354, 8621925847489749, 8307493939404888703058, 102488432265617100812550713499, 17706351554929677399562928448484650120, 46435685450659378932235460132506329282776942795

Offset

0,3

Links

Table of n, a(n) for n=0..12.

Eric Weisstein's World of Mathematics, Polygonal Number

Index entries for sequences related to compositions

Index to sequences related to polygonal numbers

Formula

a(n) = [x^p(n,n)] 1 / (1 - Sum_{k=1..n} 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) = 7 because the third triangular number is 6 and we have [6], [3, 3], [3, 1, 1, 1], [1, 3, 1, 1], [1, 1, 3, 1], [1, 1, 1, 3] and [1, 1, 1, 1, 1, 1].

Crossrefs

Cf. A011782, A060354, A224366, A224677, A337762, A337763.

Sequence in context: A070521 A292433 A338181 * A000889 A323597 A286423

Adjacent sequences: A337761 A337762 A337763 * A337765 A337766 A337767

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 19 2020

Status

approved