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A160527 Coefficients in the expansion of C^3/B^4, in Watson's notation of page 118.

%I A160527 #23 Aug 11 2025 07:05:04
%S A160527 1,4,14,40,105,252,574,1237,2568,5138,9988,18893,34937,63238,112370,
%T A160527 196244,337477,572024,956956,1581321,2583637,4176495,6684820,10599939,
%U A160527 16661401,25972485,40171474,61672695,94017765,142368024,214211760,320350725,476299978
%N A160527 Coefficients in the expansion of C^3/B^4, in Watson's notation of page 118.
%H A160527 Seiichi Manyama, <a href="/A160527/b160527.txt">Table of n, a(n) for n = 0..1000</a>
%H A160527 G. N. Watson, <a href="https://gdz.sub.uni-goettingen.de/id/PPN243919689_0179">Ramanujans Vermutung über Zerfällungsanzahlen</a>, J. Reine Angew. Math. (Crelle), 179 (1938), 97-128.
%F A160527 See Maple code in A160525 for formula.
%F A160527 G.f.: Product_{n >= 1} (1 - x^(7*n))^3/(1 - x^n)^4. - _Seiichi Manyama_, Nov 06 2016
%F A160527 a(n) ~ exp(Pi*sqrt(50*n/21)) * 5 / (196*sqrt(3)*n). - _Vaclav Kotesovec_, Nov 10 2017
%e A160527 G.f. = 1 + 4*x + 14*x^2 + 40*x^3 + 105*x^4 + 252*x^5 + 574*x^6 + ...
%e A160527 G.f. = q^17 + 4*q^41 + 14*q^65 + 40*q^89 + 105*q^113 + 252*q^137 + 574*q^161 + ...
%t A160527 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 *)
%Y A160527 Cf. A071746, A213261.
%K A160527 nonn
%O A160527 0,2
%A A160527 _N. J. A. Sloane_, Nov 13 2009