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%I #27 Feb 17 2024 15:03:49
%S 1,0,1,0,1,0,1,1,1,1,1,1,2,1,3,1,3,2,3,3,3,4,4,4,6,4,7,5,8,7,8,9,9,10,
%T 12,11,15,12,17,15,18,19,20,22,24,24,29,26,34,31,37,38,40,44,46,49,55,
%U 53,64,60,71,71,77,83,86,93,100,101,116,112,130,129,142,149,156,168,177
%N Number of partitions of n into parts each congruent to 2 mod 5.
%H Vaclav Kotesovec, <a href="/A109698/b109698.txt">Table of n, a(n) for n = 0..10000</a>
%F G.f.: 1/Product_{j>=0} (1 - x^(2+5j)). - _Emeric Deutsch_, Feb 15 2006
%F a(n) ~ Gamma(2/5) * exp(Pi*sqrt(2*n/15)) / (2^(17/10) * 3^(1/5) * 5^(3/10)*Pi^(3/5) * n^(7/10)) * (1 + (11*Pi/(120*sqrt(30)) - 7*sqrt(3/10)/(5*Pi)) / sqrt(n)). - _Vaclav Kotesovec_, Feb 27 2015, extended Jan 24 2017
%F a(n) = (1/n)*Sum_{k=1..n} A284280(k)*a(n-k), a(0) = 1. - _Seiichi Manyama_, Mar 24 2017
%e a(12)=2 since 12 = 12 = 2+2+2+2+2+2.
%p g:=1/product(1-x^(2+5*i),i=0..20): gser:=series(g,x=0,86): seq(coeff(gser,x,n),n=0..82); # _Emeric Deutsch_, Feb 15 2006
%t nmax=100; CoefficientList[Series[Product[1/(1-x^(5*k+2)),{k, 0, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Feb 27 2015 *)
%o (PARI) Vec(prod(k=0, 100, 1/(1 - x^(5*k + 2))) + O(x^111)) \\ _Indranil Ghosh_, Mar 24 2017
%Y Cf. A284280.
%K nonn
%O 0,13
%A _Erich Friedman_, Aug 07 2005
%E More terms from _Emeric Deutsch_, Feb 15 2006
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