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A000714 Number of partitions of n, with three kinds of 1 and 2 and two kinds of 3,4,5,....
(Formerly M2777 N1117)
+0
1
1, 3, 9, 21, 47, 95, 186, 344, 620, 1078, 1835, 3045, 4967, 7947, 12534, 19470, 29879, 45285, 67924, 100820, 148301, 216199, 312690, 448738, 639464, 905024, 1272837, 1779237, 2473065, 3418655, 4701611, 6434015, 8763676 (list; graph; listen)
OFFSET

0,2

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

H. Gupta et al., Tables of Partitions. Royal Society Mathematical Tables, Vol. 4, Cambridge Univ. Press, 1958, p. 122.

LINKS

N. J. A. Sloane, Transforms

FORMULA

EULER transform of 3, 3, 2, 2, 2, 2, 2, 2...

G.f.=1/[(1-x)(1-x^2)product((1-x^k)^2, k=1..infinity)]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 17 2006

EXAMPLE

a(2)=9 because we have 2, 2', 2", 1+1, 1'+1', 1"+1", 1+1', 1+1", 1'+1".

MAPLE

g:=1/((1-x)*(1-x^2)*product((1-x^k)^2, k=1..40)): gser:=series(g, x=0, 50): seq(coeff(gser, x, n), n=0..32); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 17 2006

CROSSREFS

Sequence in context: A062444 A141156 A014286 this_sequence A090984 A006813 A056823

Adjacent sequences: A000711 A000712 A000713 this_sequence A000715 A000716 A000717

KEYWORD

nonn

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

Extended with formula from Christian G. Bower (bowerc(AT)usa.net), Apr 15 1998.

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Last modified November 24 23:16 EST 2009. Contains 167481 sequences.


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