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 A007552 Exponentiation of Fibonacci numbers. (Formerly M2860) 4
 1, 3, 10, 42, 204, 1127, 6924, 46704, 342167, 2700295, 22799218, 204799885, 1947993126, 19540680497, 206001380039, 2275381566909, 26261810071925, 315969045744894, 3954454344433658, 51382626410402336, 691956435942841207 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Alois P. Heinz, Table of n, a(n) for n = 1..500 M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, arXiv:math/0205301 [math.CO], 2002. [pLink to arXiv version] M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures] FORMULA E.g.f.: exp(exp(x/2)*(sqrt(5)*cosh(x*sqrt(5)/2)+sinh(x*sqrt(5)/2))/sqrt(5)-1)-1. - Vladimir Kruchinin, Feb 27 2015 MAPLE f:= proc(n) option remember; `if`(n<2, 1, f(n-1) +f(n-2)) end: a:= proc(n) option remember; f(n) +add(binomial(n-1, k-1) *f(k) *a(n-k), k=1..n-1) end: seq(a(n), n=1..30); # Alois P. Heinz, Oct 07 2008 MATHEMATICA f[n_] := f[n] = If[n<2, 1, f[n-1]+f[n-2]]; a[n_] := a[n] = f[n]+Sum [Binomial[n-1, k-1]*f[k]*a[n-k], {k, 1, n-1}]; Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Mar 03 2014, after Alois P. Heinz *) PROG (PARI) Vec(serlaplace(exp( serconvol(Ser(1/(1-x-x^2)), exp(x))-1))) /* ==> [1, 1, 3, 10, 42, 204, 1127, 6924, 46704, ...] (note offset 0) */ /* Joerg Arndt, Jun 16 2010 */ CROSSREFS Cf. A006701, A256180. Sequence in context: A091843 A300632 A300511 * A125274 A030903 A030816 Adjacent sequences:  A007549 A007550 A007551 * A007553 A007554 A007555 KEYWORD nonn AUTHOR STATUS approved

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Last modified April 13 06:52 EDT 2021. Contains 342935 sequences. (Running on oeis4.)