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 A278555 Expansion of Product_{n>=1} (1 - x^(5*n))^12/(1 - x^n)^13 in powers of x. 11
 1, 13, 104, 637, 3276, 14808, 60541, 228124, 803010, 2667054, 8422715, 25446304, 73907808, 207209614, 562673618, 1484147681, 3811882087, 9553588317, 23407932874, 56161135485, 132132608899, 305240006266, 693150485885, 1548871015291, 3408852663762, 7395582677152 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS In general, if m>0 and g.f. = Product_{k>=1} (1 - x^(5*k))^m/(1 - x^k)^(m+1) then a(n) ~ sqrt(4*m+5) * exp(Pi*sqrt(2*(4*m+5)*n/15)) / (4*sqrt(3)*5^((m+1)/2)*n). - Vaclav Kotesovec, Nov 24 2016 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..2500 Vaclav Kotesovec, A method of finding the asymptotics of q-series based on the convolution of generating functions, arXiv:1509.08708 [math.CO], Sep 30 2015. FORMULA G.f.: Product_{n>=1} (1 - x^(5*n))^12/(1 - x^n)^13. A278559(n) = 5^2*63*A160460(n) + 5^5*52*a(n-1) + 5^7*63*A278556(n-2) + 5^10*6*A278557(n-3) + 5^12*A278558(n-4) for n >= 4. a(n) ~ sqrt(53/15)*exp(sqrt(106*n/15)*Pi)/(62500*n). - Vaclav Kotesovec, Nov 24 2016 MATHEMATICA CoefficientList[ Series[ Product[(1 - x^(5n))^12/(1 - x^n)^13, {n, 25}], {x, 0, 25}], x] (* Robert G. Wilson v, Nov 23 2016 *) CROSSREFS Cf. A160460, A278556, A278557, A278558, A278559. Sequence in context: A289859 A129762 A283121 * A282921 A023011 A022641 Adjacent sequences:  A278552 A278553 A278554 * A278556 A278557 A278558 KEYWORD nonn AUTHOR Seiichi Manyama, Nov 23 2016 STATUS approved

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Last modified November 30 22:31 EST 2021. Contains 349426 sequences. (Running on oeis4.)