cp's OEIS Frontend

A160533 Coefficients in the expansion of C^5/B^6, in Watson's notation of page 118.

%I A160533 #23 Aug 11 2025 07:35:44
%S A160533 1,6,27,98,315,918,2492,6367,15495,36145,81326,177219,375461,775544,
%T A160533 1565870,3096615,6008917,11458720,21502964,39754385,72485518,
%U A160533 130464603,231989748,407847488,709365160,1221364655,2082872680,3519963776,5897536697,9800358525
%N A160533 Coefficients in the expansion of C^5/B^6, in Watson's notation of page 118.
%H A160533 Seiichi Manyama, <a href="/A160533/b160533.txt">Table of n, a(n) for n = 0..1000</a>
%H A160533 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 A160533 See Maple code in A160525 for formula.
%F A160533 G.f.: Product_{n>=1} (1 - x^(7*n))^5/(1 - x^n)^6. - _Seiichi Manyama_, Nov 06 2016
%F A160533 a(n) ~ exp(Pi*sqrt(74*n/21)) * sqrt(37) / (1372*sqrt(3)*n). - _Vaclav Kotesovec_, Nov 10 2017
%e A160533 G.f. = 1 + 6*x + 27*x^2 + 98*x^3 + 315*x^4 + 918*x^5 + 2492*x^6 + ...
%e A160533 G.f. = q^29 + 6*q^53 + 27*q^77 + 98*q^101 + 315*q^125 + 918*q^149 + 2492*q^173 + ...
%t A160533 nn = 29; CoefficientList[Series[Product[(1 - x^(7 n))^5/(1 - x^n)^6, {n, nn}], {x, 0, nn}], x] (* _Michael De Vlieger_, Nov 06 2016 *)
%Y A160533 Cf. A160525, A160526, A160527, A160528.
%K A160533 nonn
%O A160533 0,2
%A A160533 _N. J. A. Sloane_, Nov 14 2009