A280421 G.f.: Product_{k>=1} (1 + x^(k*(k+1)/2)) / (1 - x^k).

1, 2, 3, 6, 10, 15, 24, 36, 52, 76, 109, 152, 211, 290, 393, 530, 709, 938, 1236, 1618, 2102, 2720, 3500, 4477, 5707, 7242, 9146, 11511, 14435, 18030, 22451, 27868, 34476, 42531, 52324, 64186, 78541, 95867, 116721, 141791, 171862, 207844, 250846, 302134

Offset

0,2

Comments

Convolution of A024940 and A000041.

Links

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

Formula

a(n) ~ exp(sqrt(2*n/3)*Pi + 3^(1/4) * (sqrt(2)-1) * Zeta(3/2) * n^(1/4) / 2^(3/4) + 3*(2*sqrt(2)-3) * Zeta(3/2)^2 / (32*Pi)) / (8*sqrt(3)*n).

Mathematica

nmax=60; CoefficientList[Series[Product[(1+x^(k*(k+1)/2))/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A024940, A000041, A280204, A280423.

Sequence in context: A056178 A320597 A227566 * A369425 A018141 A178659

Adjacent sequences: A280418 A280419 A280420 * A280422 A280423 A280424

Keyword

nonn

Author

Vaclav Kotesovec, Jan 02 2017

Status

approved