cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A000997 From a differential equation.

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%I A000997 M0739 N0277 #27 Oct 23 2019 12:19:07
%S A000997 0,1,0,0,1,2,3,5,12,36,110,326,963,2964,9797,34818,130585,506996,
%T A000997 2018454,8238737,34627390,150485325,677033911,3147372610,15066340824,
%U A000997 74025698886,372557932434,1919196902205,10119758506626,54627382038761,301832813494746
%N A000997 From a differential equation.
%C A000997 Shifts 3 places left under binomial transform. - _Olivier Gérard_, Aug 12 2016
%D A000997 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000997 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000997 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 A000997 G.f. A(x) satisfies: A(x) = x*(1 + x^2*A(x/(1 - x))/(1 - x)). - _Ilya Gutkovskiy_, May 02 2019
%p A000997 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 A000997 m = 30; A[_] = 0;
%t A000997 Do[A[x_] = x (1 + x^2 A[x/(1 - x)]/(1 - x)) + O[x]^m // Normal, {m}];
%t A000997 CoefficientList[A[x], x] (* _Jean-François Alcover_, Oct 23 2019 *)
%Y A000997 Cf. A000995.
%K A000997 nonn,eigen
%O A000997 0,6
%A A000997 _N. J. A. Sloane_
%E A000997 More terms from _Sean A. Irvine_, Mar 27 2015