A319256 Expansion of Product_{k>0} (1 + k*(k+1)/2 * x^(k*(k+1)/2)).

1, 1, 0, 3, 3, 0, 6, 6, 0, 18, 28, 10, 0, 30, 30, 15, 75, 60, 45, 225, 180, 111, 111, 0, 333, 483, 150, 126, 604, 478, 378, 1572, 1194, 0, 3498, 3498, 351, 2115, 2044, 1333, 4833, 4620, 2946, 2526, 2100, 8043, 11133, 9810, 5175, 13773, 13638, 810, 31194, 34584, 6630

Offset

0,4

Comments

Sum of products of terms in all partitions of n into distinct triangular numbers (A000217).

Links

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

Example

a(16) = 75 because we have [15, 1], [10, 6], 15*1 = 15, 10*6 = 60 and 15 + 60 = 75.

Crossrefs

Cf. A000217, A024940, A282866, A319257.

Sequence in context: A322215 A244492 A210838 * A354618 A117234 A122831

Adjacent sequences: A319253 A319254 A319255 * A319257 A319258 A319259

Keyword

nonn

Author

Seiichi Manyama, Sep 15 2018

Status

approved