A280424 G.f.: Product_{k>=1} (1 + x^k) / (1 - x^(k*(k+1))).

1, 1, 2, 3, 4, 6, 9, 12, 16, 22, 28, 37, 49, 62, 79, 101, 125, 157, 196, 241, 297, 365, 443, 539, 654, 787, 947, 1137, 1355, 1616, 1923, 2276, 2693, 3179, 3737, 4391, 5149, 6018, 7027, 8191, 9521, 11057, 12822, 14831, 17140, 19779, 22777, 26206, 30110, 34534

Offset

0,3

Links

Table of n, a(n) for n=0..49.

Formula

a(n) ~ exp(sqrt(n/3)*Pi + 3^(1/4) * Zeta(3/2) * n^(1/4) / sqrt(2) - 3*Zeta(3/2)^2 / (16*Pi)) / (16 * 3^(3/4) * n^(5/4)).

Mathematica

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

Crossrefs

Cf. A007294, A000009, A280422.

Sequence in context: A371178 A271147 A069907 * A083365 A001935 A286141

Adjacent sequences: A280421 A280422 A280423 * A280425 A280426 A280427

Keyword

nonn

Author

Vaclav Kotesovec, Jan 02 2017

Status

approved