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

0,4

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.

Links

Table of n, a(n) for n=0..45.

Example

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; ...

Prog

(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)}

Crossrefs

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

Sequence in context: A051190 A072512 A271531 * A259633 A174500 A249163

Adjacent sequences: A118585 A118586 A118587 * A118589 A118590 A118591

Keyword

nonn,tabl

Author

Paul D. Hanna, May 08 2006

Status

approved