A118588 - OEIS

%I #4 Mar 30 2012 18:36:57

%S 1,1,1,2,1,12,1,36,12,1,80,180,1,150,1260,120,1,252,5460,3360,1,392,

%T 17640,43680,1680,1,576,46872,342720,75600,1,810,108360,1839600,

%U 1587600,30240,1,1100,225720,7539840,20235600,1995840,1,1452,433620,25391520

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

%C 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.

%e Triangle begins:

%e 1;

%e 1;

%e 1,2;

%e 1,12;

%e 1,36,12;

%e 1,80,180;

%e 1,150,1260,120;

%e 1,252,5460,3360;

%e 1,392,17640,43680,1680;

%e 1,576,46872,342720,75600; ...

%e O.g.f. for columns:

%e 0!/0!*(1)/(1-x);

%e 2!/1!*(1+2*x)/(1-x)^4;

%e 4!/2!*(1+8*x+21*x^2)/(1-x)^7;

%e 6!/3!*(1+18*x+129*x^2+356*x^3)/(1-x)^10;

%e 8!/4!*(1+32*x+438*x^2+2984*x^3+8425*x^4)/(1-x)^13; ...

%o (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)}

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

%K nonn,tabl

%O 0,4

%A _Paul D. Hanna_, May 08 2006