A000997 From a differential equation. (Formerly M0739 N0277)

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

0,6

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

Table of n, a(n) for n=0..30.

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

Formula

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

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 *)

Crossrefs

Cf. A000995.

Sequence in context: A369847 A306038 A008323 * A266541 A301929 A107475

Adjacent sequences: A000994 A000995 A000996 * A000998 A000999 A001000

Keyword

nonn,eigen

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Mar 27 2015

Status

approved