A076687 Coefficients in asymptotic (divergent) expansion for Sum_{k=1..n} 1/C(n,k)^2.

1, 0, 2, 0, 8, 16, 96, 464, 2848, 19056, 142400, 1166608, 10411488, 100496816, 1043154304, 11585854032, 137089725728, 1721562067696, 22867314748608, 320313336833936, 4718773157942368, 72932090897154096, 1180003546791130112, 19945632339806733520, 351569488641977570208

Offset

0,3

Comments

A005649 gives asymptotic divergent expansion for Sum_{k=0..n} 1/C(n,k).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..100

Formula

Sum_{k>=1} 1/C(n, k)^2 = 1/n^0 + 0/n^1 + 2/n^2 + 0/n^3 + 8/n^4 + 16/n^5 + 96/n^6 + ...

a(m) ~ Pi * m^(m+1) / (2^(m+3) * (log(2))^(m + 3/2) * exp(m)). - Vaclav Kotesovec, May 25 2020

Example

Sum_{k=1..1000} 1/C(1000,k)^2 = 1.000002000008016096466....

Mathematica

nmax = 30; CoefficientList[1 + 2*Total[Table[Normal[Series[1/Binomial[n, k]^2, {n, Infinity, nmax}]], {k, 1, nmax/2}]], 1/n] (* Vaclav Kotesovec, May 25 2020 *)

Crossrefs

Cf. A005649.

Sequence in context: A319196 A308536 A241682 * A062134 A002909 A118437

Adjacent sequences: A076684 A076685 A076686 * A076688 A076689 A076690

Keyword

nonn

Author

Benoit Cloitre, Oct 25 2002

Extensions

Corrected and extended by Vladeta Jovovic, Oct 26 2007

Corrected by Vaclav Kotesovec, May 25 2020

Status

approved