A000998 From a differential equation. (Formerly M2549 N1009)

1, 3, 6, 11, 24, 69, 227, 753, 2451, 8004, 27138, 97806, 375313, 1511868, 6292884, 26826701, 116994453, 523646202, 2414394601, 11487130362, 56341183365, 284110648983, 1468690344087, 7766823788295, 41976012524088, 231812530642644, 1308325741771908

Offset

0,2

Comments

When preceded by {0, 0, 1, 0, 0}, this sequence shifts 3 places 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

Alois P. Heinz, Table of n, a(n) for n = 0..695

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

Formula

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

Maple

b:= proc(n) option remember; `if`(n<3, [0$2, 1][n+1],
      add(binomial(n-3, j)*b(j), j=0..n-3))
    end:
a:= n-> b(n+5):
seq(a(n), n=0..30);  # Alois P. Heinz, May 21 2019

Mathematica

b[n_] := b[n] = If[n<3, {0, 0, 1}[[n+1]], Sum[Binomial[n-3, j] b[j], {j, 0, n-3}]];
a[n_] := b[n+5];
a /@ Range[0, 30] (* Jean-François Alcover, Oct 27 2020, after Alois P. Heinz *)

Crossrefs

Sequence in context: A319636 A001867 A369691 * A331536 A365294 A221182

Adjacent sequences: A000995 A000996 A000997 * A000999 A001000 A001001

Keyword

nonn,eigen

Author

N. J. A. Sloane

Extensions

More terms from Vladeta Jovovic, Feb 05 2008

Status

approved