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A024429
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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 B sequence (cf. A024430).
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12
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0, 1, 1, 2, 7, 27, 106, 443, 2045, 10440, 57781, 340375, 2115664, 13847485, 95394573, 690495874, 5235101739, 41428115543, 341177640610, 2917641580783, 25866987547865, 237421321934176, 2252995117706961, 22073206655954547
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Number of partitions of an n-element set into an odd number of classes. - Peter Luschny, Apr 25 2011
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REFERENCES
| L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 226, 4th line of table.
A. Fekete and others, Problem 10791, Amer. Math. Monthly, 108 (No. 2, 2001), 177-178.
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
| S(n,1) + S(n,3) + ... + S(n,2k+1), where k = [ (n-1)/2 ] and S(i,j) are Stirling numbers of second kind.
E.g.f.: sinh(exp(x)-1) - N. J. A. Sloane (njas(AT)research.att.com), Jan 28, 2001
a(n) = (A000110(n) - A000587(n)) / 2. - Peter Luschny, Apr 25 2011
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CROSSREFS
| Cf. A024430, A121867, A121868, A000110, A000587.
Sequence in context: A150591 A150592 A150593 * A136412 A192417 A150594
Adjacent sequences: A024426 A024427 A024428 * A024430 A024431 A024432
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| Description changed by N. J. A. Sloane (njas(AT)research.att.com), Sep 05 2006
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