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A007548 Shifts 3 places left under exponentiation.
(Formerly M1485)
4
1, 1, 1, 1, 2, 5, 15, 53, 213, 961, 4808, 26405, 157965, 1022573, 7122441, 53118601, 422362118, 3566967917, 31887812715, 300848966213, 2987359924149, 31143724848889, 340113005563268, 3882897830626949, 46254432194746377, 573938743829923349, 7406289665830324689 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

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..200

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 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. A(x) satisfies differential equation A'''(x)=exp(A(x)), A'(0)=1, A''(0)=1, A'''(0)=1. - Vladimir Kruchinin, Nov 19 2011

MAPLE

exptr:= proc(p) local g; g:= proc(n) option remember; p(n) +add(binomial(n-1, k-1) *p(k) *g(n-k), k=1..n-1) end: end: b:= exptr(a): a:= n-> `if`(n<=2, 1, b(n-3)): seq(a(n), n=1..30); # Alois P. Heinz, Oct 07 2008

MATHEMATICA

Exptr[p_] := Module[{g}, g[n_] := g[n] = p[n] + Sum [Binomial[n-1, k-1]*p[k]*g[n-k], {k, 1, n-1}]; g]; b = Exptr [a]; a[n_] := If[n <= 2, 1, b[n-3]]; Table[a[n], {n, 1, 30}] (* Jean-Fran├žois Alcover, May 06 2014, after Alois P. Heinz *)

CROSSREFS

Sequence in context: A107589 A249892 A006790 * A120567 A263779 A125280

Adjacent sequences:  A007545 A007546 A007547 * A007549 A007550 A007551

KEYWORD

nonn,eigen

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 19 06:03 EDT 2018. Contains 316336 sequences. (Running on oeis4.)