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A117955 Number of partitions of n into exactly 2 types of odd parts. 2
0, 0, 0, 1, 1, 2, 3, 5, 4, 7, 8, 10, 11, 13, 12, 19, 18, 20, 22, 25, 24, 30, 31, 36, 33, 39, 38, 45, 45, 48, 51, 57, 54, 60, 56, 69, 67, 72, 72, 79, 78, 84, 84, 90, 87, 97, 97, 112, 99, 107, 112, 117, 115, 126, 118, 131, 134, 137, 136, 152, 143, 149, 149, 163, 152, 174, 164 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Table of n, a(n) for n=1..67.

FORMULA

G.f.=sum(sum(x^(2i+2j-2)/[(1-x^(2i-1))(1-x^(2j-1))], j=1..i-1), i=1..infinity).

G.f. for number of partitions of n into exactly m types of odd parts is obtained if we substitute x(i) with -Sum_{k>0}(x^(2*n-1)/(x^(2*n-1)-1))^i in the cycle index Z(S(m); x(1),x(2),..,x(m)) of the symmetric group S(m) of degree m. - Vladeta Jovovic, Sep 20 2007

EXAMPLE

a(8)=5 because we have [7,1],[5,3],[5,1,1,1],[3,3,1,1] and [3,3,1,1].

MAPLE

g:=sum(sum(x^(2*i+2*j-2)/(1-x^(2*i-1))/(1-x^(2*j-1)), j=1..i-1), i=1..40): gser:=series(g, x=0, 75): seq(coeff(gser, x^n), n=1..72);

CROSSREFS

Cf. A002133.

Sequence in context: A181095 A127515 A099424 * A074049 A193973 A127521

Adjacent sequences:  A117952 A117953 A117954 * A117956 A117957 A117958

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Apr 05 2006

STATUS

approved

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Last modified April 16 11:56 EDT 2014. Contains 240591 sequences.