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

0,3

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

Formula

Equals the main diagonal of triangle A187005.

Prog

(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)}

Crossrefs

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

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

Sequence in context: A089104 A007334 A050398 * A296366 A110083 A086922

Adjacent sequences: A135078 A135079 A135080 * A135082 A135083 A135084

Keyword

nonn

Author

Paul D. Hanna, Nov 18 2007

Status

approved