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

Author

Ilya Gutkovskiy, Apr 18 2019

Keywords

• nonn

Examples

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

Links

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

Crossrefs

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

Formula

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