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

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, 111, 128, 148, 170, 195, 224, 256, 293, 334, 380, 432, 491, 557, 630, 713, 805, 908, 1024, 1152, 1295, 1455, 1632, 1829, 2049, 2291, 2560, 2859, 3189, 3554, 3958, 4404

Offset: 1

Author

Reinhard Zumkeller, Apr 22 2006

Keywords

• nonn

Comments

a(2*n) = A026838(2*n), a(2*n-1) = A026837(2*n-1);

a(n) = A000009(n) - A118302(n);

a(A090864(n)) = A118303(n)/2 = A000009(A090864(n))/2.

Examples

			a(11) = #{11,9+2,7+4,7+3+1,5+4+2,5+3+2+1} = 6;
a(12) = #{12,10+2,8+4,8+3+1,6+5+1,6+4+2,6+3+2+1} = 7.
		

Crossrefs

Cf. A046682, A118302.

Formula

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