A099765 a(n) = (1/Pi)*(2^n/n)*(n-1)!*Integral_{t>=0} (sin(t)/t)^n dt.

1, 1, 2, 8, 46, 352, 3364, 38656, 519446, 7996928, 138826588, 2683604992, 57176039628, 1331300646912, 33636118326984, 916559498182656, 26795449170328038, 836606220759859200, 27784046218331805100

Offset: 1

Author

Benoit Cloitre, Nov 11 2004, Dec 11 2007

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..406
• 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

Crossrefs

Cf. A049330, A261398.

Programs

Magma

[(1/n)*(&+[(-1)^j*Binomial(n,j)*(n-2*j)^(n-1): j in [0..Floor(n/2)]]): n in [1..25]]; // G. C. Greubel, Apr 01 2022

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 *)

PARI

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

Sage

[(1/n)*sum((-1)^j*binomial(n,j)*(n-2*j)^(n-1) for j in (0..(n//2))) for n in (1..25)] # G. C. Greubel, Apr 01 2022

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