A320352 Expansion of e.g.f. (exp(x) - 1)/(exp(x) - exp(2*x) + 1).

0, 1, 3, 19, 159, 1651, 20583, 299419, 4977759, 93097891, 1934655063, 44224195819, 1102820674959, 29792843865331, 866769668577543, 27018340680076219, 898343366411181759, 31736205208791131971, 1187110673532381604023, 46871464129796857140619, 1948059531745350527058159

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..401

Formula

E.g.f.: (1 + sinh(x) - cosh(x))/(1 - 2*sinh(x)).

a(n) = Sum_{k=0..n} Stirling2(n,k)*Fibonacci(k)*k!.

a(n) ~ n! / (sqrt(5) * phi^2 * (log(phi))^(n+1)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Oct 12 2018

Maple

seq(n!*coeff(series((exp(x) - 1)/(exp(x) - exp(2*x) + 1), x=0, 22), x, n), n=0..21); # Paolo P. Lava, Jan 09 2019

Mathematica

nmax = 20; CoefficientList[Series[(Exp[x] - 1)/(Exp[x] - Exp[2 x] + 1), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS2[n, k] Fibonacci[k] k!, {k, 0, n}], {n, 0, 20}]

Crossrefs

Cf. A000045, A000556, A000557, A005443, A005445, A048993, A263576.

Sequence in context: A077046 A232607 A307697 * A301921 A054765 A362660

Adjacent sequences: A320349 A320350 A320351 * A320353 A320354 A320355

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 11 2018

Status

approved