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A118301 Number of partitions of n into distinct parts with largest part congruent to n modulo 2. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

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.

LINKS

Table of n, a(n) for n=1..58.

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

EXAMPLE

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.

Sequence in context: A094983 A238218 A015744 * A018121 A256636 A258327

Adjacent sequences:  A118298 A118299 A118300 * A118302 A118303 A118304

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Apr 22 2006

STATUS

approved

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Last modified May 12 03:08 EDT 2021. Contains 343810 sequences. (Running on oeis4.)