A007548 Shifts 3 places left under exponentiation. (Formerly M1485)

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

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]

Ronald Orozco López, Solution of the Differential Equation y^(k)= e^(a*y), Special Values of Bell Polynomials and (k,a)-Autonomous Coefficients, Universidad de los Andes (Colombia 2021).

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-François Alcover, May 06 2014, after Alois P. Heinz *)

Crossrefs

Sequence in context: A249892 A352853 A006790 * A360052 A328431 A120567

Adjacent sequences: A007545 A007546 A007547 * A007549 A007550 A007551

Keyword

nonn,eigen

Author

N. J. A. Sloane.

Status

approved