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, 977999315746501427200, 36372399938142060650276, 1425145264171451810840576

Offset

1,3

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]

Walter 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

a(n) ~ sqrt(3) * (2/e)^n * n^(n-2). - Amiram Eldar, Apr 22 2026

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))
(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
(SageMath) [(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

Crossrefs

Cf. A049330, A261398.

Sequence in context: A300696 A074599 A007289 * A385367 A246386 A096656

Adjacent sequences: A099762 A099763 A099764 * A099766 A099767 A099768

Keyword

nonn

Author

Benoit Cloitre, Nov 11 2004, Dec 11 2007

Status

approved