A307614 Number of partitions of the n-th triangular number into consecutive positive triangular numbers.

1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1

Offset

1,4

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Formula

a(n) = [x^(n*(n+1)/2)] Sum_{i>=1} Sum_{j>=i} Product_{k=i..j} x^(k*(k+1)/2).

Example

A000217(4) = 10 = 1 + 3 + 6, so a(4) = 2.

Crossrefs

Cf. A000217, A034706, A072964, A196010, A288126, A298858, A307608.

Sequence in context: A348416 A263025 A184348 * A363057 A242481 A228287

Adjacent sequences: A307611 A307612 A307613 * A307615 A307616 A307617

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 18 2019

Status

approved