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A279358 Exponential transform of the cubes A000578.

%I A279358 #20 Feb 16 2025 08:33:37
%S A279358 1,1,9,52,413,3916,41077,481384,6198425,86430160,1296040841,
%T A279358 20763245944,353272341061,6353672109760,120315348389069,
%U A279358 2390488408994536,49682962883210033,1077292416660660736,24313317132393295633,569937590287796925784,13850459183086300341341
%N A279358 Exponential transform of the cubes A000578.
%H A279358 Alois P. Heinz, <a href="/A279358/b279358.txt">Table of n, a(n) for n = 0..479</a>
%H A279358 M. Bernstein and N. J. A. Sloane, <a href="https://arxiv.org/abs/math/0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
%H A279358 M. Bernstein and N. J. A. Sloane, <a href="/A003633/a003633_1.pdf">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
%H A279358 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A279358 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ExponentialTransform.html">Exponential Transform</a>
%H A279358 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CubicNumber.html">Cubic Number</a>
%F A279358 E.g.f.: exp(exp(x)*(x+3*x^2+x^3)).
%e A279358 E.g.f.: A(x) = 1 + x/1! + 9*x^2/2! + 52*x^3/3! + 413*x^4/4! + 3916*x^5/5! + 41077*x^6/6! + ...
%p A279358 a:= proc(n) option remember; `if`(n=0, 1,
%p A279358       add(binomial(n-1, j-1)*j^3*a(n-j), j=1..n))
%p A279358     end:
%p A279358 seq(a(n), n=0..25);  # _Alois P. Heinz_, Dec 11 2016
%t A279358 Range[0, 20]! CoefficientList[Series[Exp[Exp[x] (x + 3 x^2 + x^3)], {x, 0, 20}], x]
%Y A279358 Cf. A000578, A033462.
%Y A279358 Column k=3 of A279636.
%K A279358 nonn
%O A279358 0,3
%A A279358 _Ilya Gutkovskiy_, Dec 10 2016