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A109697 Number of partitions of n into parts each equal to 1 mod 5.

%I A109697 #29 Jul 17 2019 17:13:27
%S A109697 1,1,1,1,1,1,2,2,2,2,2,3,4,4,4,4,5,6,7,7,7,8,10,11,12,12,13,15,17,18,
%T A109697 19,20,23,26,28,29,31,34,38,41,43,45,50,55,60,63,66,71,79,85,90,94,
%U A109697 101,110,120,127,133,141,153,165,176,184,195,210,227,241,254,267,286,307,327
%N A109697 Number of partitions of n into parts each equal to 1 mod 5.
%H A109697 Vaclav Kotesovec, <a href="/A109697/b109697.txt">Table of n, a(n) for n = 0..10000</a>
%F A109697 G.f.: 1/product(1-x^(1+5j), j=0..infinity). - _Emeric Deutsch_, Mar 30 2006
%F A109697 a(n) ~ Gamma(1/5) * exp(Pi*sqrt(2*n/15)) / (2^(8/5) * 3^(1/10) * 5^(2/5) * Pi^(4/5) * n^(3/5)) * (1 - (3*sqrt(3/10)/(5*Pi) + Pi/(120*sqrt(30))) / sqrt(n)). - _Vaclav Kotesovec_, Feb 27 2015, extended Jan 24 2017
%F A109697 a(n) = (1/n)*Sum_{k=1..n} A284097(k)*a(n-k), a(0) = 1. - _Seiichi Manyama_, Mar 20 2017
%F A109697 G.f.: Sum_{k>=0} x^k / Product_{j=1..k} (1 - x^(5*j)). - _Ilya Gutkovskiy_, Jul 17 2019
%e A109697 a(11)=3 since 11 = 11 = 6+1+1+1+1+1 = 1+1+1+1+1+1+1+1+1+1+1
%p A109697 g:=1/product(1-x^(1+5*j),j=0..25): gser:=series(g,x=0,85): seq(coeff(gser,x,n),n=0..80); # _Emeric Deutsch_, Mar 30 2006
%t A109697 Table[Count[IntegerPartitions[n],_?(Union[Mod[#,5]]=={1}&)],{n,0,75}] (* _Harvey P. Dale_, Oct 08 2011 *)
%Y A109697 Cf. A000041, A003105, A284097.
%Y A109697 Cf. similar sequences of number of partitions of n into parts congruent to 1 mod m: A000009 (m=2), A035382 (m=3), A035451 (m=4), this sequence (m=5), A109701 (m=6), A109703 (m=7), A277090 (m=8).
%K A109697 nonn
%O A109697 0,7
%A A109697 _Erich Friedman_, Aug 07 2005
%E A109697 More terms from _Emeric Deutsch_, Mar 30 2006