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%I #17 Mar 20 2017 12:46:54
%S 1,0,0,0,1,0,0,0,1,1,0,0,1,1,1,0,1,1,2,1,1,1,2,2,2,1,2,3,4,2,2,3,5,4,
%T 3,3,6,6,6,4,6,7,9,7,7,8,11,11,11,9,12,14,16,13,14,16,21,20,19,18,24,
%U 26,27,24,27,31,36,34,34,35,43,45,47,43,49,55,62,58,59,63,75,77,77,75,87
%N Number of partitions of n into parts each equal to 4 mod 5.
%H Vaclav Kotesovec, <a href="/A109700/b109700.txt">Table of n, a(n) for n = 0..10000</a>
%F G.f.: 1/product(1-x^(4+5j), j=0..infinity). - _Emeric Deutsch_, Mar 30 2006
%F a(n) ~ Gamma(4/5) * exp(Pi*sqrt(2*n/15)) / (2^(19/10) * 3^(2/5) * 5^(1/10) * Pi^(1/5) * n^(9/10)) * (1 - (9*sqrt(6/5)/(5*Pi) + Pi/(120*sqrt(30))) / sqrt(n)). - _Vaclav Kotesovec_, Feb 27 2015, extended Jan 24 2017
%F a(n) = (1/n)*Sum_{k=1..n} A284103(k)*a(n-k), a(0) = 1. - _Seiichi Manyama_, Mar 20 2017
%e a(30)=2 since 30 = 14+4+4+4+4 = 9+9+4+4+4
%p g:=1/product(1-x^(4+5*j),j=0..25): gser:=series(g,x=0,95): seq(coeff(gser,x,n),n=0..90); # _Emeric Deutsch_, Mar 30 2006
%t nmax=100; CoefficientList[Series[Product[1/(1-x^(5*k+4)), {k, 0, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Feb 27 2015 *)
%Y Cf. A284103.
%Y Cf. similar sequences of number of partitions of n into parts congruent to m-1 mod m: A000009 (m=2), A035386 (m=3), A035462 (m=4), this sequence (m=5), A109702 (m=6), A109708 (m=7).
%K nonn
%O 0,19
%A _Erich Friedman_, Aug 07 2005
%E More terms from _Michael Somos_, Aug 10 2005
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