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 A007550 Natural numbers exponentiated twice. (Formerly M3568) 9
 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 STATUS approved

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Last modified May 9 05:11 EDT 2021. Contains 343688 sequences. (Running on oeis4.)