A280949 Expansion of Product_{k>=1} (1 - x^(12*k)) * (1 - x^(4*k-2)) / (1 - x^k).

1, 1, 1, 2, 3, 4, 5, 7, 10, 13, 16, 21, 27, 34, 42, 53, 67, 82, 100, 123, 151, 183, 220, 266, 321, 384, 457, 545, 649, 768, 906, 1069, 1260, 1478, 1729, 2023, 2363, 2751, 3196, 3711, 4304, 4978, 5747, 6631, 7641, 8787, 10089, 11575, 13266, 15177, 17340

Offset

0,4

Links

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

Andrew Sills, Towards an Automation of the Circle Method, Gems in Experimental Mathematics in Contemporary Mathematics, 2010, formula S110.

Formula

a(n) ~ 2*Pi * BesselI(1, sqrt(8*n+3)*Pi/(3*sqrt(2))) / (3*sqrt(24*n+9)).

a(n) ~ exp(2*Pi*sqrt(n)/3) / (3*2^(3/2)*n^(3/4)) * (1 + (Pi/8 - 9/(16*Pi))/sqrt(n) + (Pi^2/128 - 135/(512*Pi^2) - 45/128)/n).

Mathematica

nmax=50; CoefficientList[Series[Product[(1-x^(12*k))*(1-x^(4*k-2))/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Sequence in context: A071682 A014670 A036034 * A316718 A316719 A316720

Adjacent sequences: A280946 A280947 A280948 * A280950 A280951 A280952

Keyword

nonn

Author

Vaclav Kotesovec, Jan 11 2017

Status

approved