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A117955 Number of partitions of n into exactly 2 types of odd parts. 5
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

REFERENCES

N. BENYAHIA TANI, S. BOUROUBI, O. KIHEL, An effective approach for integer partitions using exactly two distinct sizes of parts, Bulletin du Laboratoire, 03 (2015) 18 - 27; Availaible on line at http://www.liforce.usthb.dz.

D Christopher, T Nadu, Partitions with Fixed Number of Sizes, Journal of Integer Sequences, 15 (2015), #15.11.5.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

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: A127515 A256996 A099424 * A074049 A193973 A245057

Adjacent sequences:  A117952 A117953 A117954 * A117956 A117957 A117958

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Apr 05 2006

STATUS

approved

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Last modified December 7 13:07 EST 2016. Contains 278875 sequences.