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A189087
E.g.f.: sinh(x)/(1-sinh(x)-sinh(x)^2).
1
1, 2, 13, 80, 721, 7232, 87613, 1193600, 18431041, 315130112, 5936395213, 121904337920, 2712867153361, 65005861947392, 1669061195146813, 45709411009495040, 1330071346341607681, 40979304201240707072, 1332713597815933766413, 45623097880495676456960
OFFSET
1,2
LINKS
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
Cf. A000045.
Sequence in context: A000179 A335700 A246383 * A037739 A037634 A074581
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Apr 20 2011
STATUS
approved