OFFSET
0,4
LINKS
Nathaniel Johnston, Table of n, a(n) for n = 0..60
FORMULA
G.f.: Sum(Sum((-1)^(n-k)*binomial(n,k)*((1+x)^(k-1)-1)^k*((1+x)^k-1)^(n-k),k=0..n),n=0..infinity).
a(n) ~ c * n! / (sqrt(n) * (log(2))^(2*n)), where c = 0.0722246614111436... . - Vaclav Kotesovec, May 07 2014
In closed form, c = 1/(sqrt(Pi*(1-log(2))) * log(2) * 2^(4+log(2)/2)). - Vaclav Kotesovec, May 04 2015
MAPLE
n:=20: t:=taylor(sum(sum((-1)^(m-k)*binomial(m, k)*((1+x)^(k-1)-1)^k*((1+x)^k-1)^(m-k), k=0..m), m=0..n), x, n+1): seq(coeff(t, x, m), m=0..n); # Nathaniel Johnston, Apr 28 2011
MATHEMATICA
Flatten[{1, Rest[CoefficientList[Series[Sum[Sum[(-1)^(n-k)*Binomial[n, k]*((1+x)^(k-1)-1)^k*((1+x)^k-1)^(n-k), {k, 0, n}], {n, 1, 20}], {x, 0, 20}], x]]}] (* Vaclav Kotesovec, May 07 2014 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Sep 02 2006
STATUS
approved