A000996 Shifts 3 places left under binomial transform. (Formerly M1618 N0632)

1, 0, 0, 1, 1, 1, 2, 6, 17, 44, 112, 304, 918, 3040, 10623, 38161, 140074, 528594, 2068751, 8436893, 35813251, 157448068, 713084042, 3315414747, 15805117878, 77273097114, 387692392570, 1996280632656, 10542604575130, 57034787751655, 315649657181821

Offset

0,7

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..300

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210; arXiv:math/0205301 [math.CO], 2002.

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]

N. J. A. Sloane, Transforms

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

Formula

G.f. A(x) satisfies: A(x) = 1 + x^3 * A(x/(1 - x)) / (1 - x). - Ilya Gutkovskiy, Aug 09 2020

Maple

a:= proc(n) option remember; local k; if n<=2 then [1, 0, 0][n+1] else 1+ add(binomial(n-3, k) *a(k), k=3..n-3) fi end: seq(a(n), n=0..29); # Alois P. Heinz, Sep 05 2008

Mathematica

a[n_] := a[n] = If[n <= 2 , {1, 0, 0}[[n+1]], 1+Sum [Binomial[n-3, k]*a[k], {k, 3, n-3}]]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 24 2014, after Alois P. Heinz *)

Crossrefs

Column k=3 of A143983.

Sequence in context: A018024 A364450 A190159 * A309757 A020963 A065068

Adjacent sequences: A000993 A000994 A000995 * A000997 A000998 A000999

Keyword

nonn,eigen

Author

N. J. A. Sloane

Extensions

More terms from Alois P. Heinz, Sep 05 2008

Status

approved