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A103264 Number of partitions of n into distinct parts prime to 3, 5 and 7. 0

%I

%S 1,1,1,1,1,1,1,1,1,1,1,2,2,3,3,3,3,4,4,5,5,5,6,7,8,8,9,9,10,11,13,14,

%T 15,16,18,19,21,23,24,26,28,31,34,37,39,42,45,49,53,56,60,64,69,75,81,

%U 86,92,98,105,113,122,130,138,147,157,168,179,191,202,215,230,246,262,279

%N Number of partitions of n into distinct parts prime to 3, 5 and 7.

%F G.f.: product_{k>0}((1+x^k)*(1+x^(15k))*(1+x^(21k))*(1+x^(35k)))/((1+x^(3k))*(1+x^(5k))*(1+x^(7k))*(1+x^(105k))).

%F a(n) ~ exp(4*Pi*sqrt(n/105)) / (sqrt(2) * 105^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Sep 07 2015

%e a(19)=5 because 19 = 17 + 2 = 16 + 2 + 1 = 13 + 4 + 2 = 11 + 8.

%p series(product((1+x^k)*(1+x^(15*k))*(1+x^(21*k))*(1+x^(35*k)))/((1+x^(3*k))*(1+x^(5*k))*(1+x^(7*k))*(1+x^(105*k))),k=1..100),x=0,100);

%t CoefficientList[ Series[ Product[(1 + x^k)(1 + x^(15k))(1 + x^(21k))(1 + x^(35k))/((1 + x^(3k))(1 + x^(5k))(1 + x^(7k))(1 + x^(105k))), {k, 100}], {x, 0, 73}], x] (* _Robert G. Wilson v_, Feb 22 2005 *)

%K nonn

%O 0,12

%A _Noureddine Chair_, Feb 21 2005

%E More terms from _Robert G. Wilson v_, Feb 22 2005

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Last modified April 15 20:40 EDT 2021. Contains 342977 sequences. (Running on oeis4.)