A172383 a(0)=1, otherwise a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n-k-1,k)*a(n-1-2*k).

1, 1, 1, 2, 4, 8, 19, 46, 118, 322, 903, 2653, 8053, 25194, 81387, 269667, 917529, 3197480, 11393821, 41497060, 154186653, 584151512, 2254240317, 8852998343, 35361762709, 143540660088, 591802631729, 2476701062087

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..932

Formula

G.f. A(x) satisfies: A(x) = 1 + (x/(1-x^2)) * A(x/(1-x^2)).

Example

Eigensequence for number triangle
  1;
  1,  0;
  0,  1,  0;
  1,  0,  1,  0;
  0,  2,  0,  1,  0;
  1,  0,  3,  0,  1,  0;
  0,  3,  0,  4,  0,  1,  0;
  1,  0,  6,  0,  5,  0,  1,  0;
  0,  4,  0, 10,  0,  6,  0,  1,  0;
  1,  0, 10,  0, 15,  0,  7,  0,  1,  0;
  0,  5,  0, 20,  0, 21,  0,  8,  0,  1,  0;
(augmented version of Riordan array (1/(1-x^2), x/(1-x^2)), A030528.

Maple

A172383 := proc(n)
    option remember;
    if n = 0 then
        1;
    else
        add(binomial(n-k-1, k)*procname(n-1-2*k), k=0..floor((n-1)/2)) ;
    end if;
end proc:
seq(A172383(n), n=0..20) ; # R. J. Mathar, Feb 11 2015

Mathematica

a[n_]:= If[n == 0, 1, Sum[Binomial[n-k-1, k]*a[n-2*k-1], {k, 0, Floor[(n-1)/2]}]]; Table[a[n], {n, 0, 30}] (* G. C. Greubel, Oct 07 2018 *)

Crossrefs

Cf. A030528.

Sequence in context: A151526 A099526 A005703 * A003081 A100133 A099598

Adjacent sequences: A172380 A172381 A172382 * A172384 A172385 A172386

Keyword

easy,nonn

Author

Paul Barry, Feb 01 2010

Extensions

Name corrected by R. J. Mathar, Feb 11 2015

Status

approved