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A261638 Expansion of Product_{k>=0} (1+x^(4*k+1))^4. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 26 08:18 EST 2020. Contains 331278 sequences. (Running on oeis4.)