A185523 a(n) equals the coefficient of x^n in the n-th iteration of x*(1+x)/(1-x) for n>=1.

1, 4, 30, 368, 6370, 143372, 3983518, 131891776, 5073152322, 222405974228, 10948833767454, 598115891581232, 35907789570992898, 2350053890768819484, 166532363675821702206, 12703556005092777381120, 1037944178579609842602754

Offset: 1

Author

Paul D. Hanna, Jan 30 2011

Keywords

• nonn

Examples

			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), ...]; ...;
the coefficients in parenthesis form the initial terms of this sequence.
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A185522, A185524.

Programs

PARI

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