cp's OEIS Frontend

A118301 Number of partitions of n into distinct parts with largest part congruent to n modulo 2.

%I A118301 #10 Feb 14 2021 13:12:44
%S A118301 1,1,1,1,2,2,2,3,4,5,6,7,9,11,13,16,19,23,27,32,38,44,52,61,71,83,96,
%T A118301 111,128,148,170,195,224,256,293,334,380,432,491,557,630,713,805,908,
%U A118301 1024,1152,1295,1455,1632,1829,2049,2291,2560,2859,3189,3554,3958,4404
%N A118301 Number of partitions of n into distinct parts with largest part congruent to n modulo 2.
%C A118301 a(2*n) = A026838(2*n), a(2*n-1) = A026837(2*n-1);
%C A118301 a(n) = A000009(n) - A118302(n);
%C A118301 a(A090864(n)) = A118303(n)/2 = A000009(A090864(n))/2.
%F A118301 Conjectural g.f.: A(x) = Limit_{N -> oo} ( Sum_{n = 0..2*N+1} (-1)^(n+1)/Product_{k = 1..n} 1 - x^(2*k-1) ). - _Peter Bala_, Feb 11 2021
%e A118301 a(11) = #{11,9+2,7+4,7+3+1,5+4+2,5+3+2+1} = 6;
%e A118301 a(12) = #{12,10+2,8+4,8+3+1,6+5+1,6+4+2,6+3+2+1} = 7.
%Y A118301 Cf. A046682, A118302.
%K A118301 nonn
%O A118301 1,5
%A A118301 _Reinhard Zumkeller_, Apr 22 2006