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Search: id:A079491
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| A079491 |
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Numerator of Sum(binomial(n,k)/2^(k*(k-1)/2), k = 0 .. n). |
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+0
3
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| 1, 2, 7, 45, 545, 12625, 564929, 49162689, 8361575425, 2789624383745, 1830776926245889, 2368773751202917377, 6053217182280501452801, 30595465072175429929979905, 306239118989330960523869667329, 6076268165073202122463201684865025
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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D. L. Kreher and D. R. Stinson, Combinatorial Algorithms, CRC Press, 1999, p. 113.
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FORMULA
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E.g.f.: Sum_{n>=0} a(n)*x^n/n! = Sum_{n>=0} exp(2^n*x)*2^(n(n-1)/2)*x^n/n!. [From Paul D. Hanna (pauldhanna(AT)juno.com), Sep 14 2009]
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EXAMPLE
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1, 2, 7/2, 45/8, 545/64, 12625/1024, 564929/32768, 49162689/2097152, ...
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MAPLE
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f := n->add(binomial(n, k)/2^(k*(k-1)/2), k=0..n);
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PROGRAM
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(PARI) {a(n)=n!*polcoeff(sum(k=0, n, exp(2^k*x +x*O(x^n))*2^(k*(k-1)/2)*x^k/k!), n)} [From Paul D. Hanna (pauldhanna(AT)juno.com), Sep 14 2009]
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CROSSREFS
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Denominators are in A006125.
Cf. A079492.
Sequence in context: A098637 A162045 A153549 this_sequence A162046 A162047 A162048
Adjacent sequences: A079488 A079489 A079490 this_sequence A079492 A079493 A079494
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KEYWORD
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nonn,frac
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jan 20 2003
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