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Search: id:A024430
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| A024430 |
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Let A(0) = 1, B(0) = 0; A(n+1) = Sum_{k=0..n} binomial(n,k)*B(k), B(n+1) = Sum_{k=0..n} binomial(n,k)*A(k); entry gives A sequence (cf. A024429). |
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13
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| 1, 0, 1, 3, 8, 25, 97, 434, 2095, 10707, 58194, 338195, 2097933, 13796952, 95504749, 692462671, 5245040408, 41436754261, 340899165549, 2915100624274, 25857170687507, 237448494222575, 2253720620740362, 22078799199129799, 222987346441156585
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Number of partitions of an n-element set into an even number of classes.
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 226, 5th line of table.
A. Fekete and others, Problem 10791, Amer. Math. Monthly, 108 (No. 2, 2001), 177-178.
L. Lovasz, Combinatorial Problems and Exercises, North-Holland, 1993, pp. 15, 148.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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a(n) = S(n, 2) + S(n, 4) + ... + S(n, 2k), where k = [ n/2 ], S(i, j) are Stirling numbers of second kind.
E.g.f.: cosh(exp(x)-1) - N. J. A. Sloane (njas(AT)research.att.com), Jan 28, 2001
a(n)=sum(stirling2(n,2*i), i=0..n,n>=0 . - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 31 2008
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MAPLE
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with(combinat):seq(sum(stirling2(n, 2*i), i=0..n), n=0..24); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 31 2008
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CROSSREFS
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Cf. A024429, A121867, A121868.
Sequence in context: A130522 A006219 A009268 this_sequence A012408 A051403 A004205
Adjacent sequences: A024427 A024428 A024429 this_sequence A024431 A024432 A024433
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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Description changed by N. J. A. Sloane (njas(AT)research.att.com), Jun 14 2003 and again Sep 05 2006
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