A261638 Expansion of Product_{k>=0} (1+x^(4*k+1))^4.

1, 4, 6, 4, 1, 4, 16, 24, 16, 8, 22, 48, 52, 32, 38, 92, 128, 96, 70, 140, 245, 244, 172, 228, 417, 488, 374, 380, 680, 924, 798, 676, 1044, 1560, 1542, 1256, 1625, 2524, 2778, 2304, 2537, 3892, 4716, 4156, 4076, 5908, 7650, 7196, 6592, 8796, 11938

Offset

0,2

Comments

In general, if j > 0, a > 0, b > 0, GCD(a,b) = 1 and g.f. = Product_{k>=0} (1 + x^(a*k+b))^j, then a(n) ~ 2^((j-3)/2 - j*b/a) * j^(1/4) * exp(Pi*sqrt(j*n/(3*a))) / ((3*a)^(1/4) * n^(3/4)).

Links

Table of n, a(n) for n=0..50.

Formula

a(n) ~ exp(Pi*sqrt(n/3)) / (sqrt(2) * 3^(1/4) * n^(3/4)).

Mathematica

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

Crossrefs

Cf. A261612, A261615, A261637, A169975, A261630, A261634.

Sequence in context: A087108 A021687 A063422 * A010670 A240444 A199358

Adjacent sequences: A261635 A261636 A261637 * A261639 A261640 A261641

Keyword

nonn

Author

Vaclav Kotesovec, Aug 27 2015

Status

approved