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%I #16 Mar 28 2017 14:48:25
%S 1,0,0,0,1,0,0,0,1,0,0,1,1,0,0,1,1,0,1,1,1,0,2,1,1,1,2,1,1,2,2,1,2,3,
%T 2,1,4,3,2,2,5,3,2,4,6,3,3,6,6,3,6,7,6,4,9,8,6,7,11,8,7,11,12,8,11,14,
%U 13,9,16,16,13,13,21,17,14,20,24,18,19,26,26,19,27,31,27,24,36,34,29,34,43
%N Number of partitions of n into parts each equal to 4 mod 7.
%H Vaclav Kotesovec, <a href="/A109706/b109706.txt">Table of n, a(n) for n = 0..10000</a>
%F G.f.: 1/product(1-x^(4+7j), j=0..infinity). - _Emeric Deutsch_, Apr 14 2006
%F a(n) ~ Gamma(4/7) * exp(Pi*sqrt(2*n/21)) / (2^(25/14) * 3^(2/7) * 7^(3/14) * Pi^(3/7) * n^(11/14)) * (1 + (23*Pi/(168*sqrt(42)) - 11*sqrt(6/7)/(7*Pi)) / sqrt(n)). - _Vaclav Kotesovec_, Feb 27 2015, extended Jan 24 2017
%F a(n) = (1/n)*Sum_{k=1..n} A284445(k)*a(n-k), a(0) = 1. - _Seiichi Manyama_, Mar 28 2017
%e a(22)=2 because we have 22=18+4=11+11.
%p g:=1/product(1-x^(4+7*j),j=0..20): gser:=series(g,x=0,93): seq(coeff(gser,x,n),n=0..90); # _Emeric Deutsch_, Apr 14 2006
%t nmax=100; CoefficientList[Series[Product[1/(1-x^(7*k+4)),{k, 0, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Feb 27 2015 *)
%K nonn
%O 0,23
%A _Erich Friedman_, Aug 07 2005
%E Changed offset to 0 and added a(0)=1 by _Vaclav Kotesovec_, Feb 27 2015
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