A118082 Number of partitions of n such that largest part k occurs floor(k/2) times.

1, 0, 1, 2, 2, 3, 3, 4, 5, 6, 8, 10, 12, 15, 19, 22, 27, 32, 39, 45, 54, 63, 75, 87, 102, 118, 139, 160, 186, 214, 248, 284, 328, 375, 430, 490, 561, 637, 727, 824, 935, 1058, 1199, 1352, 1528, 1720, 1938, 2177, 2448, 2743, 3079, 3445, 3856, 4307, 4813, 5365, 5985

Offset

0,4

Comments

Also number of partitions of n such that if the number of parts is k, then the smallest part is floor(k/2). Example: a(8)=5 because we have [7,1],[6,1,1],[5,2,1],[4,3,1] and [2,2,2,2].

Links

Table of n, a(n) for n=0..56.

Formula

G.f.=sum(x^(k*floor(k/2))/product(1-x^j, j=1..k-1), k=1..infinity).

Example

a(8)=5 because we have [4,4],[3,2,2,1],[3,2,1,1,1],[3,1,1,1,1,1] and [2,1,1,1,1,1,1].

Maple

g:=sum(x^(k*floor(k/2))/product(1-x^j, j=1..k-1), k=1..15): gser:=series(g, x=0, 65): seq(coeff(gser, x, n), n=0..60);

Crossrefs

Cf. A118083, A118084.

Sequence in context: A005686 A328675 A365072 * A120160 A017980 A064650

Adjacent sequences: A118079 A118080 A118081 * A118083 A118084 A118085

Keyword

nonn

Author

Emeric Deutsch, Apr 12 2006

Status

approved