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A000998 From a differential equation.

%I A000998 M2549 N1009 #25 Oct 27 2020 08:48:08
%S A000998 1,3,6,11,24,69,227,753,2451,8004,27138,97806,375313,1511868,6292884,
%T A000998 26826701,116994453,523646202,2414394601,11487130362,56341183365,
%U A000998 284110648983,1468690344087,7766823788295,41976012524088,231812530642644,1308325741771908
%N A000998 From a differential equation.
%C A000998 When preceded by {0, 0, 1, 0, 0}, this sequence shifts 3 places under binomial transform. - _Olivier Gérard_, Aug 12 2016
%D A000998 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000998 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000998 Alois P. Heinz, <a href="/A000998/b000998.txt">Table of n, a(n) for n = 0..695</a>
%H A000998 S. Tauber, <a href="http://www.jstor.org/stable/2308653">On generalizations of the exponential function</a>, Amer. Math. Monthly, 67 (1960), 763-767.
%F A000998 G.f.: A(x) = Sum(x^(3*k-3)/Product(1-l*x,l = 0 .. k)^3,k = 0 .. infinity). - _Vladeta Jovovic_, Feb 05 2008
%p A000998 b:= proc(n) option remember; `if`(n<3, [0$2, 1][n+1],
%p A000998       add(binomial(n-3, j)*b(j), j=0..n-3))
%p A000998     end:
%p A000998 a:= n-> b(n+5):
%p A000998 seq(a(n), n=0..30);  # _Alois P. Heinz_, May 21 2019
%t A000998 b[n_] := b[n] = If[n<3, {0, 0, 1}[[n+1]], Sum[Binomial[n-3, j] b[j], {j, 0, n-3}]];
%t A000998 a[n_] := b[n+5];
%t A000998 a /@ Range[0, 30] (* _Jean-François Alcover_, Oct 27 2020, after _Alois P. Heinz_ *)
%K A000998 nonn,eigen
%O A000998 0,2
%A A000998 _N. J. A. Sloane_
%E A000998 More terms from _Vladeta Jovovic_, Feb 05 2008