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 A278680 Expansion of Product_{n>=1} (1 - x^(5*n))/(1 - x^n)^4 in powers of x. 2
 1, 4, 14, 40, 105, 251, 570, 1226, 2540, 5075, 9855, 18630, 34439, 62340, 110805, 193624, 333235, 565415, 947040, 1567130, 2564425, 4152535, 6658711, 10579380, 16663755, 26033200, 40357641, 62106290, 94912385, 144088840, 217368655, 325945320, 485950150, 720515475 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..1000 FORMULA G.f.: Product_{n>=1} (1 - x^(5*n))/(1 - x^n)^4. a(n) ~ 19 * exp(Pi*sqrt(38*n/15)) / (120 * sqrt(10) * n^(3/2)). - Vaclav Kotesovec, Nov 10 2017 EXAMPLE G.f.: 1 + 4*x + 14*x^2 + 40*x^3 + 105*x^4 + 251*x^5 + 570*x^6 + ... MATHEMATICA nmax = 30; CoefficientList[Series[Product[(1 - x^(5*k))/(1 - x^k)^4, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 10 2017 *) CROSSREFS Cf. Product_{n>=1} (1 - x^(5*n))/(1 - x^n)^k: A035959 (k=1), A160461 (k=2), A278668 (k=3), this sequence (k=4), A277212 (k=5), A182821 (k=6). Sequence in context: A066368 A274327 A160463 * A121593 A160527 A023003 Adjacent sequences:  A278677 A278678 A278679 * A278681 A278682 A278683 KEYWORD nonn AUTHOR Seiichi Manyama, Nov 25 2016 STATUS approved

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Last modified January 17 16:39 EST 2019. Contains 319235 sequences. (Running on oeis4.)