A000997 From a differential equation.

0, 1, 0, 0, 1, 2, 3, 5, 12, 36, 110, 326, 963, 2964, 9797, 34818, 130585, 506996, 2018454, 8238737, 34627390, 150485325, 677033911, 3147372610, 15066340824, 74025698886, 372557932434, 1919196902205, 10119758506626, 54627382038761, 301832813494746

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• eigen

Comments

Shifts 3 places left under binomial transform. - Olivier Gérard, Aug 12 2016

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• S. Tauber, On generalizations of the exponential function, Amer. Math. Monthly, 67 (1960), 763-767.

Crossrefs

Cf. A000995.

Programs

Maple

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

Mathematica

m = 30; A[_] = 0;
Do[A[x_] = x (1 + x^2 A[x/(1 - x)]/(1 - x)) + O[x]^m // Normal, {m}];
CoefficientList[A[x], x] (* Jean-François Alcover, Oct 23 2019 *)

Formula

G.f. A(x) satisfies: A(x) = x*(1 + x^2*A(x/(1 - x))/(1 - x)). - Ilya Gutkovskiy, May 02 2019

Extensions

More terms from Sean A. Irvine, Mar 27 2015