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Search: id:A052847
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| A052847 |
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G.f.: Product_{k>=1} (1-x^k)^(-k+1). |
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+0
4
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| 1, 0, 1, 2, 4, 6, 12, 18, 33, 52, 88, 138, 229, 354, 568, 880, 1378, 2110, 3260, 4942, 7527, 11320, 17031, 25394, 37842, 55956, 82630, 121300, 177677, 258980, 376626, 545352, 787784, 1133764, 1627657, 2329020, 3324559, 4731396, 6717774, 9512060
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Euler transform of sequence [0,1,2,3,...]. - Michael Somos Jul 2 2004
Number of partitions of n objects of 2 colors, where each part must contain at least one of each color. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jan 23 2006.
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 815
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FORMULA
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a(n) = 1/n*Sum_{k=1..n} (sigma[2](k)-sigma[1](k))*a(n-k).
G.f.: exp( Sum_{k>0} ( x^k / (1 - x^k) )^2 / k ).
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EXAMPLE
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1 + x^2 + 2*x^3 + 4*x^4 + 6*x^5 + 12*x^6 + 18*x^7 + 33*x^8 + 52*x^9 + ...
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MAPLE
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spec := [S, {B=Sequence(Z, 1 <= card), C=Prod(B, B), S= Set(C)}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
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PROGRAM
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(PARI) {a(n) = if( n<0, 0, polcoeff( 1 / prod(k=1, n, (1 - x^k + x*O(x^n))^(k-1)), n))}
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CROSSREFS
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Cf. A005380, A000203, A001157.
Cf. A052812.
Sequence in context: A060735 A051683 A007436 this_sequence A052823 A063516 A104352
Adjacent sequences: A052844 A052845 A052846 this_sequence A052848 A052849 A052850
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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Edited by Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 10 2002
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