A000998 From a differential equation.

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

Author

N. J. A. Sloane

Keywords

• nonn
• eigen

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.

Programs

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 *)

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

Extensions

More terms from Vladeta Jovovic, Feb 05 2008