OFFSET
0,3
COMMENTS
Sequence is signed: first negative term is a(35) = -230450728485788167742674544892530875760640. - Vladeta Jovovic, Sep 29 2003
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Georg Fischer, Table of n, a(n) for n = 0..100
P. R. J. Asveld & N. J. A. Sloane, Correspondence, 1987
P. R. J. Asveld, Fibonacci-like differential equations with a polynomial nonhomogeneous term, Fib. Quart. 27 (1989), 303-309.
FORMULA
a(n) = Sum_{k=0..n} k!*Fibonacci(k+1)*Stirling1(n, k).
E.g.f.: 1/(1 - log(1+x) - log(1+x)^2). - Vladeta Jovovic, Sep 29 2003
a(n) ~ n! * (-1)^n * exp(n*(1+sqrt(5))/2) / (sqrt(5)*(exp((1+sqrt(5))/2)-1)^(n+1)). - Vaclav Kotesovec, Oct 01 2013
MATHEMATICA
CoefficientList[Series[1/(1-Log[1+x]-(Log[1+x])^2), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 01 2013 *)
PROG
(PARI) a(n) = sum(k=0, n, k!*fibonacci(k+1)*stirling(n, k, 1)); \\ Michel Marcus, Oct 30 2015
(Magma) [(&+[Factorial(j)*Fibonacci(j+1)*StirlingFirst(n, j): j in [0..n]]): n in [0..30]]; // G. C. Greubel, Nov 21 2022
(SageMath)
def A005444(n): return sum((-1)^(n+k)*factorial(k)*fibonacci(k+1)* stirling_number1(n, k) for k in (0..n))
[A005444(n) for n in range(31)] # G. C. Greubel, Nov 21 2022
CROSSREFS
KEYWORD
sign,easy
AUTHOR
STATUS
approved