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A005444 From a Fibonacci-like differential equation.
(Formerly M2766)
0
1, 1, 3, 8, 50, 214, 2086, 11976, 162816, 1143576, 20472504, 165910128, 3785092032, 33908109936, 967508478192, 9252123203712, 327062428940160, 3236057604910080, 141403289873955840, 1404243298160352000, 76168955916831029760, 735206146073008508160 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..21.

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!*fibonacci(k + 1)*stirling1(n, k), k = 0..n).

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

CROSSREFS

Sequence in context: A019015 A000862 A194364 * A222684 A208801 A019044

Adjacent sequences:  A005441 A005442 A005443 * A005445 A005446 A005447

KEYWORD

sign,easy

AUTHOR

Simon Plouffe, N. J. A. Sloane.

STATUS

approved

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Last modified November 22 05:36 EST 2017. Contains 295076 sequences.