A280423 G.f.: Product_{k>=1} (1 + x^(k*(k+1))) / (1 - x^k).

1, 1, 3, 4, 7, 10, 17, 23, 36, 49, 71, 96, 136, 180, 248, 326, 437, 569, 752, 967, 1261, 1609, 2069, 2620, 3335, 4189, 5285, 6595, 8249, 10230, 12706, 15661, 19327, 23696, 29063, 35457, 43256, 52519, 63756, 77073, 93126, 112120, 134901, 161781, 193884, 231679

Offset

0,3

Links

Table of n, a(n) for n=0..45.

Formula

a(n) ~ exp(sqrt(2*n/3)*Pi + 3^(1/4) * (sqrt(2)-1) * Zeta(3/2) * n^(1/4) / 2^(5/4) + 3*(2*sqrt(2)-3) * Zeta(3/2)^2 / (64*Pi)) / (8*sqrt(3)*n).

Mathematica

nmax=60; CoefficientList[Series[Product[(1+x^(k*(k+1)))/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A024940, A000041, A280421.

Sequence in context: A357459 A098613 A261037 * A143607 A193826 A032715

Adjacent sequences: A280420 A280421 A280422 * A280424 A280425 A280426

Keyword

nonn

Author

Vaclav Kotesovec, Jan 02 2017

Status

approved