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A160527
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Coefficients in the expansion of C^3/B^4, in Watson's notation of page 118.
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6
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1, 4, 14, 40, 105, 252, 574, 1237, 2568, 5138, 9988, 18893, 34937, 63238, 112370, 196244, 337477, 572024, 956956, 1581321, 2583637, 4176495, 6684820, 10599939, 16661401, 25972485, 40171474, 61672695, 94017765, 142368024, 214211760, 320350725, 476299978
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OFFSET
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0,2
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LINKS
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FORMULA
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See Maple code in A160525 for formula.
G.f.: Product_{n >= 1} (1 - x^(7*n))^3/(1 - x^n)^4. - Seiichi Manyama, Nov 06 2016
a(n) ~ exp(Pi*sqrt(50*n/21)) * 5 / (196*sqrt(3)*n). - Vaclav Kotesovec, Nov 10 2017
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EXAMPLE
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G.f. = 1 + 4*x + 14*x^2 + 40*x^3 + 105*x^4 + 252*x^5 + 574*x^6 + ...
G.f. = q^17 + 4*q^41 + 14*q^65 + 40*q^89 + 105*q^113 + 252*q^137 + 574*q^161 + ...
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MATHEMATICA
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nmax = 50; CoefficientList[Series[Product[(1 - x^(7*k))^3 /(1 - x^k)^4, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 10 2017 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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