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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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12
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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; 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 even number of classes.
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REFERENCES
| 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
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
| 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) = (A000110(n) + A000587(n)) / 2. - Peter Luschny, Apr 25 2011
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CROSSREFS
| Cf. A024429, A121867, A121868, A000110, A000587.
Sequence in context: A130522 A006219 A009268 * A182927 A012408 A184325
Adjacent sequences: A024427 A024428 A024429 * A024431 A024432 A024433
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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), Jun 14 2003 and again Sep 05 2006
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