cp's OEIS Frontend

A281245 Expansion of Product_{k>=1} (1 + x^(7*k-1)).

%I A281245 #13 Nov 24 2020 10:24:05
%S A281245 1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,0,2,
%T A281245 1,0,0,0,0,1,2,1,0,0,0,0,1,3,1,0,0,0,0,2,3,1,0,0,0,0,3,4,1,0,0,0,1,4,
%U A281245 4,1,0,0,0,1,5,5,1,0,0,0,2,7,5,1,0,0,0
%N A281245 Expansion of Product_{k>=1} (1 + x^(7*k-1)).
%H A281245 Vaclav Kotesovec, <a href="/A281245/b281245.txt">Table of n, a(n) for n = 0..10000</a>
%F A281245 a(n) ~ exp(sqrt(n/21)*Pi) / (2^(13/7)*21^(1/4)*n^(3/4)) * (1 + (13*Pi/(336*sqrt(21)) - 3*sqrt(21)/(8*Pi)) / sqrt(n)). - _Vaclav Kotesovec_, Jan 18 2017, extended Jan 24 2017
%F A281245 G.f.: Sum_{k>=0} x^(k*(7*k + 5)/2) / Product_{j=1..k} (1 - x^(7*j)). - _Ilya Gutkovskiy_, Nov 24 2020
%t A281245 nmax = 200; CoefficientList[Series[Product[(1 + x^(7*k - 1)), {k, 1, nmax}], {x, 0, nmax}], x]
%t A281245 nmax = 200; poly = ConstantArray[0, nmax + 1]; poly[[1]] = 1; poly[[2]] = 0; Do[If[Mod[k, 7] == 6, Do[poly[[j + 1]] += poly[[j - k + 1]], {j, nmax, k, -1}]; ], {k, 2, nmax}]; poly
%Y A281245 Cf. A262928, A147599, A281243, A281244.
%Y A281245 Cf. A261612, A169975, A280454.
%Y A281245 Cf. A109708, A281455, A281456, A281457, A281458, A280457, A281459.
%K A281245 nonn
%O A281245 0,34
%A A281245 _Vaclav Kotesovec_, Jan 18 2017