A118588 Triangle generated by e.g.f.: A(x,y) = exp(x + y*(x^2+x^3)), read by rows of length [n/2+1].

1, 1, 1, 2, 1, 12, 1, 36, 12, 1, 80, 180, 1, 150, 1260, 120, 1, 252, 5460, 3360, 1, 392, 17640, 43680, 1680, 1, 576, 46872, 342720, 75600, 1, 810, 108360, 1839600, 1587600, 30240, 1, 1100, 225720, 7539840, 20235600, 1995840, 1, 1452, 433620, 25391520

Offset: 0

Author

Paul D. Hanna, May 08 2006

Keywords

• nonn
• tabl

Comments

E.g.f. V(x) of eigenvector A119013 satisfies: V(x) = exp(x)*V(x^2+x^3); note the similarity to e.g.f. of this triangle.

Examples

			Triangle begins:
1;
1;
1,2;
1,12;
1,36,12;
1,80,180;
1,150,1260,120;
1,252,5460,3360;
1,392,17640,43680,1680;
1,576,46872,342720,75600; ...
O.g.f. for columns:
0!/0!*(1)/(1-x);
2!/1!*(1+2*x)/(1-x)^4;
4!/2!*(1+8*x+21*x^2)/(1-x)^7;
6!/3!*(1+18*x+129*x^2+356*x^3)/(1-x)^10;
8!/4!*(1+32*x+438*x^2+2984*x^3+8425*x^4)/(1-x)^13; ...
		

Crossrefs

Cf. A118589 (row sums), A119013 (eigenvector).

Programs

PARI

{T(n,k)=n!*polcoeff(polcoeff(exp(x+y*(x^2+x^3)+x*O(x^n)+y*O(y^k)),n,x),k,y)}