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A099765 a(n) = (1/Pi)*(2^n/n)*(n-1)!*Integral_{t>=0} (sin(t)/t)^n dt. 2
1, 1, 2, 8, 46, 352, 3364, 38656, 519446, 7996928, 138826588, 2683604992, 57176039628, 1331300646912, 33636118326984, 916559498182656, 26795449170328038, 836606220759859200, 27784046218331805100 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..19.

Sergey Fomin and Grigory Mikhalkin, Labeled floor diagrams for plane curves, arXiv:0906.3828 [math.AG], 2009-2010.  [From N. J. A. Sloane, Sep 27 2010]

W. Trump, Magic series.

Eric Weisstein's World of Mathematics, Sinc Function

FORMULA

a(n) = (1/n)*sum(k=0, floor(n/2), (-1)^k*binomial(n, k)*(n-2*k)^(n-1))

a(n) = A261398(n)/n. - Vladimir Reshetnikov, Sep 05 2016

MATHEMATICA

Table[1/n Sum[(-1)^k Binomial[n, k](n-2k)^(n-1), {k, 0, Floor[n/2]}], {n, 20}] (* Harvey P. Dale, Oct 21 2011 *)

PROG

(PARI) a(n)=(1/n)*sum(k=0, floor(n/2), (-1)^k*binomial(n, k)*(n-2*k)^(n-1))

CROSSREFS

Cf. A049330.

Sequence in context: A300696 A074599 A007289 * A246386 A096656 A297014

Adjacent sequences:  A099762 A099763 A099764 * A099766 A099767 A099768

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Nov 11 2004, Dec 11 2007

STATUS

approved

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Last modified July 17 14:44 EDT 2019. Contains 325106 sequences. (Running on oeis4.)