A135081 - OEIS

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

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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