A124430 Eigenvector of triangle A124428.

1, 1, 2, 3, 7, 13, 31, 61, 144, 296, 714, 1534, 3761, 8303, 20495, 46115, 114461, 261445, 651114, 1503207, 3749017, 8726147, 21788311, 51072555, 127698665, 301244477, 754496298, 1790598079, 4494019431, 10726676701, 26983034009

Offset: 0

Author

Paul D. Hanna, Oct 31 2006

Keywords

• nonn

Examples

			a(5) = 1*a(0) + 6*a(1) + 3*a(2) = 1*1 + 6*1 + 3*2 = 13;
a(6) = 1*a(0) + 9*a(1) + 9*a(2) + 1*a(3) = 1*1 + 9*1 + 9*2 + 1*3 = 31.
Triangle A124428(n,k) = C([n/2],k)*C([(n+1)/2],k) begins:
  1;
  1;
  1,  1;
  1,  2;
  1,  4,  1;
  1,  6,  3;
  1,  9,  9,  1;
  1, 12, 18,  4;
  1, 16, 36, 16,  1; ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A124428, A124429.

Programs

Mathematica

a[n_]:= a[n] = If[n==0, 1, Sum[Binomial[Floor[n/2], k]*Binomial[Floor[(n + 1)/2], k]*a[k], {k,0,Floor[n/2]}]]; Table[a[n], {n, 0, 30}] (* G. C. Greubel, Feb 24 2019 *)

PARI

{a(n)=if(n==0,1,sum(k=0,n\2,a(k)*binomial(n\2,k)*binomial((n+1)\2,k)))}

Formula

a(n) = Sum_{k=0..[n/2]} a(k)*C([n/2],k)*C([(n+1)/2],k) for n>0, with a(0)=1 and [] means floor().