A000997 - OEIS

%I M0739 N0277 #27 Oct 23 2019 12:19:07

%S 0,1,0,0,1,2,3,5,12,36,110,326,963,2964,9797,34818,130585,506996,

%T 2018454,8238737,34627390,150485325,677033911,3147372610,15066340824,

%U 74025698886,372557932434,1919196902205,10119758506626,54627382038761,301832813494746

%N From a differential equation.

%C Shifts 3 places left under binomial transform. - _Olivier Gérard_, Aug 12 2016

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H 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 G.f. A(x) satisfies: A(x) = x*(1 + x^2*A(x/(1 - x))/(1 - x)). - _Ilya Gutkovskiy_, May 02 2019

%p a := proc(n) option remember; local k; if n<=2 then [0, 1, 0][n+1] else add (binomial(n-3, k)*a(k), k=1..n-3) fi end: seq(a(n), n=0..29); # _Sean A. Irvine_, Mar 27 2015

%t m = 30; A[_] = 0;

%t Do[A[x_] = x (1 + x^2 A[x/(1 - x)]/(1 - x)) + O[x]^m // Normal, {m}];

%t CoefficientList[A[x], x] (* _Jean-François Alcover_, Oct 23 2019 *)

%Y Cf. A000995.

%K nonn,eigen

%O 0,6

%A _N. J. A. Sloane_

%E More terms from _Sean A. Irvine_, Mar 27 2015