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A007550 Natural numbers exponentiated twice.
(Formerly M3568)
6
1, 4, 20, 127, 967, 8549, 85829, 962308, 11895252, 160475855, 2343491207, 36795832297, 617662302441, 11031160457672, 208736299803440, 4169680371133507, 87648971646028515, 1933298000313801349, 44633323736412392093, 1076069422794010119112 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The subsequence of primes (for n = 4, 5, 7) begins: 127, 967, 85829. The subsequence of semiprimes (for n = 2, 6) begins: 4, 8549. - Jonathan Vos Post, Feb 09 2011

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]

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 166

N. J. A. Sloane, Transforms

FORMULA

E.g.f.: exp(G(x) - 1) - 1, where G(x) = exp(x*exp(x)) = e.g.f. for A000248; clarified by Ilya Gutkovskiy, Jun 25 2018

a(n) = sum( k^(n - k) binomial(n,k) bell(k), k = 0..n ). - Olivier Gérard, Oct 24 2007

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: a:= exptr(exptr(n->n)): seq(a(n), n=1..30); # Alois P. Heinz, Oct 07 2008

MATHEMATICA

a[n_] := Sum[k^(n-k)*Binomial[n, k]*BellB[k], {k, 0, n}]; Table[a[n], {n, 1, 20}] (* Jean-François Alcover, Feb 11 2014, after Olivier Gérard *)

CROSSREFS

Sequence in context: A285868 A266490 A135886 * A080795 A126674 A196557

Adjacent sequences:  A007547 A007548 A007549 * A007551 A007552 A007553

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 22 15:52 EST 2019. Contains 320399 sequences. (Running on oeis4.)