A135081 Column 0 of triangle A135080.

1, 1, 2, 8, 50, 436, 4912, 68098, 1122952, 21488640, 468331252, 11456367820, 310888085872, 9269621420284, 301268634277760, 10601062978739338, 401550210033474420, 16291237867482727084, 704847239600911931248

Offset: 0

Author

Paul D. Hanna, Nov 18 2007

Keywords

• nonn

Comments

Triangle A135080 transforms diagonals in the table of coefficients of successive iterations of x+x^2 (cf. A122888).

Triangle A187005 is defined by: A187005(n,k) = [y^k] R_{n-1}(y+y^2) for k=1..n where R_n(y) is the n-th row polynomial for n>1 with R_1(y)=y.

Links

• Paul D. Hanna, Table of n, a(n) for n=0..50

Crossrefs

Cf. A135080 (triangle); other columns: A135082, A135083.

Cf. A187005, A187006, A187007, A187008, A187009.

Programs

PARI

/* As column 0 of triangle A135080 (slower): */
{a(n)=local(F=x,M,N,P); M=matrix(n+2,n+2,r,c,F=x;for(i=1,r+c-2,F=subst(F,x,x+x^2+x*O(x^(n+2))));polcoeff(F,c)); N=matrix(n+1,n+1,r,c,M[r,c]);P=matrix(n+1,n+1,r,c,M[r+1,c]);(P~*N~^-1)[n+1,1]}

PARI

/* As the main diagonal of triangle A187005 (faster): */
{a(n)=local(Rn=y); for(m=1, n+1, Rn=subst(truncate(Rn), y, y+y^2+y*O(y^m))); polcoeff(Rn/y, n, y)}

Formula

Equals the main diagonal of triangle A187005.