A281243 - OEIS

%I #18 Nov 24 2020 02:23:11

%S 1,0,0,0,1,0,0,0,0,1,0,0,0,1,1,0,0,0,1,1,0,0,0,2,1,0,0,1,2,1,0,0,1,3,

%T 1,0,0,2,3,1,0,0,3,4,1,0,1,4,4,1,0,1,5,5,1,0,2,7,5,1,0,3,8,6,1,0,5,10,

%U 6,1,1,6,12,7,1,1,9,14,7,1,2,11,16,8,1

%N Expansion of Product_{k>=1} (1 + x^(5*k-1)).

%C Convolution of this sequence and A280454 is A203776.

%H Vaclav Kotesovec, <a href="/A281243/b281243.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ exp(sqrt(n/15)*Pi) / (2^(9/5)*15^(1/4)*n^(3/4)) * (1 + (Pi/(240*sqrt(15)) - 3*sqrt(15)/(8*Pi)) / sqrt(n)). - _Vaclav Kotesovec_, Jan 18 2017, extended Jan 24 2017

%F G.f.: Sum_{k>=0} x^(k*(5*k + 3)/2) / Product_{j=1..k} (1 - x^(5*j)). - _Ilya Gutkovskiy_, Nov 24 2020

%t nmax = 200; CoefficientList[Series[Product[(1 + x^(5*k - 1)), {k, 1, nmax}], {x, 0, nmax}], x]

%t nmax = 200; poly = ConstantArray[0, nmax + 1]; poly[[1]] = 1; poly[[2]] = 0; Do[If[Mod[k, 5] == 4, Do[poly[[j + 1]] += poly[[j - k + 1]], {j, nmax, k, -1}]; ], {k, 2, nmax}]; poly

%Y Cf. A262928, A147599, A281244, A281245.

%Y Cf. A261612, A169975, A280454, A280456, A280457.

%K nonn

%O 0,24

%A _Vaclav Kotesovec_, Jan 18 2017