OFFSET
1,2
LINKS
Robert Israel, Table of n, a(n) for n = 1..413
FORMULA
a(n) = sum(k=1..n, sum(i=0..k, (-1)^i*(k-2*i)^n * binomial(k,i)) / (2^k) * A000045(k)).
a(n) ~ n! * sqrt(5-sqrt(5))/(5*sqrt(2))/(arcsinh(sqrt(5)/2-1/2))^(n+1). - Vaclav Kotesovec, Jun 27 2013
MAPLE
h:= sinh(x)/(1-sinh(x)-sinh(x)^2):
S:= series(h, x, 61):
seq(coeff(S, x, j)*j!, j=1..60); # Robert Israel, Jun 23 2017
MATHEMATICA
CoefficientList[Series[Sinh[x]/(1-Sinh[x]-Sinh[x]^2), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 27 2013 *)
PROG
(Maxima)
a(n):=sum(sum((-1)^i*(k-2*i)^n*binomial(k, i), i, 0, k)/(2^k)*fib(k), k, 1, n);
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Apr 20 2011
STATUS
approved