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A079491 Numerator of Sum_{k=0..n} binomial(n,k)/2^(k*(k-1)/2). 4
1, 2, 7, 45, 545, 12625, 564929, 49162689, 8361575425, 2789624383745, 1830776926245889, 2368773751202917377, 6053217182280501452801, 30595465072175429929979905, 306239118989330960523869667329, 6076268165073202122463201684865025 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

D. L. Kreher and D. R. Stinson, Combinatorial Algorithms, CRC Press, 1999, p. 113.

LINKS

Table of n, a(n) for n=0..15.

FORMULA

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!. - Paul D. Hanna, Sep 14 2009

EXAMPLE

1, 2, 7/2, 45/8, 545/64, 12625/1024, 564929/32768, 49162689/2097152, ...

MAPLE

f := n->add(binomial(n, k)/2^(k*(k-1)/2), k=0..n);

PROG

(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)} \\ Paul D. Hanna, Sep 14 2009

CROSSREFS

Denominators are in A006125.

Cf. A079492.

Sequence in context: A098637 A162045 A153549 * A266908 A162046 A162047

Adjacent sequences:  A079488 A079489 A079490 * A079492 A079493 A079494

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, Jan 20 2003

STATUS

approved

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Last modified May 25 19:58 EDT 2019. Contains 323576 sequences. (Running on oeis4.)