A281455 - OEIS

%I #7 Jan 24 2017 09:56:41

%S 1,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,0,0,1,0,1,0,0,0,0,2,0,1,

%T 0,0,1,0,2,0,1,0,0,1,0,3,0,1,0,0,2,0,3,0,1,0,0,3,0,4,0,1,1,0,4,0,4,0,

%U 1,1,0,5,0,5,0,1,2,0,7,0,5,0,1,3,0,8,0

%N Expansion of Product_{k>=1} (1 + x^(7*k-2)).

%H Vaclav Kotesovec, <a href="/A281455/b281455.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ exp(sqrt(n/21)*Pi) / (2^(12/7)*21^(1/4)*n^(3/4)) * (1 - (3*sqrt(21)/(8*Pi) + 11*Pi/(336*sqrt(21))) / sqrt(n)). - _Vaclav Kotesovec_, Jan 22 2017, extended Jan 24 2017

%t nmax = 100; CoefficientList[Series[Product[(1 + x^(7*k - 2)), {k, 1, nmax}], {x, 0, nmax}], x]

%t nmax = 100; poly = ConstantArray[0, nmax + 1]; poly[[1]] = 1; poly[[2]] = 0; Do[If[Mod[k, 7] == 5, Do[poly[[j + 1]] += poly[[j - k + 1]], {j, nmax, k, -1}]; ], {k, 2, nmax}]; poly

%Y Cf. A109707, A281245, A281456, A281457, A281458, A280457.

%K nonn

%O 0,32

%A _Vaclav Kotesovec_, Jan 22 2017