A321481 Expansion of Sum_{n>=1} q^(n*(n-1)) / (1-q)^n.

1, 1, 2, 3, 4, 5, 7, 10, 14, 19, 25, 32, 41, 53, 69, 90, 117, 151, 193, 244, 306, 382, 476, 593, 739, 921, 1147, 1426, 1768, 2184, 2687, 3293, 4022, 4899, 5955, 7228, 8764, 10618, 12855, 15551, 18794, 22685, 27340, 32893, 39500, 47344, 56641, 67647, 80666, 96059, 114254, 135757, 161164, 191174, 226603, 268399

Offset: 0

Author

Joerg Arndt, Nov 11 2018

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A098132 (expansion of Sum_{n>=0} q^(n*(n+1)) / (1-q)^n ).

Cf. A063978.

Programs

Mathematica

nmax = 60; CoefficientList[Series[Sum[x^(k*(k-1))/(1-x)^k, {k, 1, Sqrt[nmax] + 1}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 11 2018 *)

PARI

N=66; q='q+O('q^N); Vec( sum(n=1,N,q^(n*(n-1))/(1-q)^n) )

Formula

G.f.: Sum_{n>=1} q^(n*(n-1)) / (1-q)^n.