A185524 a(n) equals the coefficient of x^n in the (n+1)-th iteration of x*(1+x)/(1-x) for n>=1.

1, 6, 56, 770, 14272, 335846, 9623280, 325812162, 12743851808, 565954103110, 28147009533480, 1550288951887650, 93697417382512608, 6166356881177224390, 439006462312153564128, 33620884878446290152706, 2756259421284677015952320

Offset

1,2

Links

Table of n, a(n) for n=1..17.

Example

 Given G(x) = x*(1+x)/(1-x):
G(x) = x + 2*x^2 + 2*x^3 + 2*x^4 + 2*x^5 + 2*x^6 +...
then the initial coefficients of the n-th iterations of G(x) begin:
n=1: [1, 2, 2, 2, 2, 2, 2, 2, 2, ...];
n=2: [(1), 4, 12, 32, 80, 196, 476, 1152, 2784, ...];
n=3: [1,(6), 30, 138, 602, 2542, 10518, 42994, ...];
n=4: [1, 8,(56), 368, 2320, 14216, 85368, 505312, ...];
n=5: [1, 10, 90,(770), 6370, 51450, 408202, 3194978, ...];
n=6: [1, 12, 132, 1392,(14272), 143372, 1418004, 13854368, ...];
n=7: [1, 14, 182, 2282, 27930,(335846), 3983518, 46736466, ...];
n=8: [1, 16, 240, 3488, 49632, 695312,(9623280), 131891776, ...];
n=9: [1, 18, 306, 5058, 82050, 1312626, 20771730,(325812162), ...]; ...;
the coefficients in parenthesis form the initial terms of this sequence.

Prog

 (PARI) {a(n)=local(A=x, G=x*(1+x)/(1-x+x*O(x^n))); for(i=1, n+1, A=subst(G, x, A+x*O(x^n))); polcoeff(A, n)}

Crossrefs

Cf. A185522, A185523.

Sequence in context: A093197 A303921 A052317 * A122743 A241031 A268760

Adjacent sequences: A185521 A185522 A185523 * A185525 A185526 A185527

Keyword

nonn

Author

Paul D. Hanna, Jan 30 2011

Status

approved