A281666 Expansion of Sum_{i>=1} x^(i*(i+1)/2)/(1 + x^(i*(i+1)/2)) * Product_{j>=1} (1 + x^(j*(j+1)/2)).

1, 0, 1, 2, 0, 1, 2, 0, 2, 4, 2, 0, 2, 3, 1, 4, 3, 2, 6, 4, 3, 5, 0, 5, 9, 3, 2, 7, 6, 3, 11, 10, 0, 9, 12, 3, 11, 10, 8, 11, 8, 9, 9, 6, 12, 19, 15, 7, 15, 16, 4, 20, 21, 10, 23, 24, 10, 16, 19, 18, 20, 20, 17, 24, 27, 18, 28, 26, 19, 33, 30, 12, 33, 39, 25, 36, 38, 16, 32, 44, 29, 41, 48, 37, 41, 45, 33, 39, 44, 41

Offset

1,4

Comments

Total number of parts in all partitions of n into distinct nonzero triangular numbers (A000217).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Index entries for related partition-counting sequences

Formula

G.f.: Sum_{i>=1} x^(i*(i+1)/2)/(1 + x^(i*(i+1)/2)) * Product_{j>=1} (1 + x^(j*(j+1)/2)).

Example

a(10) = 4 because we have [10], [6, 3, 1] and 1 + 3 = 4.

Mathematica

nmax = 90; Rest[CoefficientList[Series[Sum[x^(i (i + 1)/2)/(1 + x^(i (i + 1)/2)), {i, 1, nmax}] Product[1 + x^(j (j + 1)/2), {j, 1, nmax}], {x, 0, nmax}], x]]

Crossrefs

Cf. A000217, A015723, A024940, A281542, A281615, A329801.

Sequence in context: A321457 A029299 A309953 * A049803 A331843 A330635

Adjacent sequences: A281663 A281664 A281665 * A281667 A281668 A281669

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 26 2017

Status

approved