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A279763 Expansion of Product_{k>=1} 1/(1 - x^k)^(k*(3*k-1)*(3*k-2)/2). 0
1, 1, 21, 105, 535, 2670, 12996, 59546, 266875, 1161894, 4939778, 20528320, 83636061, 334496221, 1315381029, 5091782355, 19424086781, 73092029218, 271537720562, 996656173345, 3616680935702, 12983391870459, 46133749660407, 162337625047433, 565962994479384, 1955721907216420, 6701061533668542, 22774651422340672 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Euler transform of the dodecahedral numbers (A006566).

LINKS

Table of n, a(n) for n=0..27.

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]

N. J. A. Sloane, Transforms

OEIS Wiki, Platonic numbers

FORMULA

G.f.: Product_{k>=1} 1/(1 - x^k)^(k*(3*k-1)*(3*k-2)/2).

a(n) ~ exp(Zeta'(-1) + 9*Zeta(3) / (8*Pi^2) - Pi^16 / (9331200000*Zeta(5)^3) + Pi^8 * Zeta(3) / (648000*Zeta(5)^2) - Zeta(3)^2 / (270*Zeta(5)) + 9*Zeta'(-3)/2 + (-Pi^12/(10800000 * 2^(2/5) * 3^(3/5) * Zeta(5)^(11/5)) + Pi^4 * Zeta(3) / (900 * 2^(2/5) * 3^(3/5) * Zeta(5)^(6/5))) * n^(1/5) + (-Pi^8 / (36000 * 2^(4/5) * 3^(1/5) * Zeta(5)^(7/5)) + Zeta(3) / (2^(4/5) * 3^(6/5) * Zeta(5)^(2/5))) * n^(2/5) + (-Pi^4 / (60 * 2^(1/5) * 3^(4/5) * Zeta(5)^(3/5))) * n^(3/5) + ((5*3^(3/5) * Zeta(5)^(1/5)) / 2^(8/5)) * n^(4/5)) * 3^(131/400) * Zeta(5)^(131/1200) / (2^(169/600) * sqrt(5*Pi) * n^(731/1200)). - Vaclav Kotesovec, Nov 09 2017

MATHEMATICA

nmax=27; CoefficientList[Series[Product[1/(1 - x^k)^(k (3 k - 1) (3 k - 2)/2), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A000335, A006566, A023872.

Sequence in context: A060537 A116689 A235876 * A068986 A219631 A226742

Adjacent sequences:  A279760 A279761 A279762 * A279764 A279765 A279766

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 18 2016

STATUS

approved

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Last modified February 25 23:44 EST 2020. Contains 332270 sequences. (Running on oeis4.)