A184900 a(n) equals the coefficient of x^(2n-1) in the (2n-1)-th iteration of x+x^3 for n>=1.

1, 3, 30, 588, 17550, 708840, 36195159, 2237012232, 162374762574, 13540681147257, 1275717308712000, 134010130947557040, 15530163914778879015, 1968213292803618315390, 270798818519865663526320

Offset: 1

Author

Paul D. Hanna, Feb 01 2011

Keywords

• nonn

Examples

			The coefficients of x^(2k-1), k>=1, in the n-th iterations of x+x^3 begin:
n=1: [(1), 1, 0, 0, 0, 0, 0, 0, ...];
n=2: [1, 2, 3, 3, 1, 0, 0, 0, ...];
n=3: [1,(3), 9, 24, 54, 102, 156, 192, ...];
n=4: [1, 4, 18, 78, 315, 1182, 4107, 13215, ...];
n=5: [1, 5,(30), 180, 1045, 5835, 31269, 160824, ...];
n=6: [1, 6, 45, 345, 2610, 19320, 139524, 982356, ...];
n=7: [1, 7, 63,(588), 5481, 50505, 458304, 4090128, ...];
n=8: [1, 8, 84, 924, 10234, 112812, 1232070, 13306902, ...];
n=9: [1, 9, 108, 1368,(17550), 225162, 2874186, 36420552, ...];
n=10:[1, 10, 135, 1935, 28215, 412920, 6031188, 87691068, ...];
n=11:[1, 11, 165, 2640, 43120,(708840), 11657448, 191245032, ...];
n=12:[1, 12, 198, 3498, 63261, 1154010, 21100233, 385492701, ...];
n=13:[1, 13, 234, 4524, 89739, 1798797,(36195159), 728702832, ...];
n=14:[1, 14, 273, 5733, 123760, 2703792, 59372040, 1305870384, ...];
n=15:[1, 15, 315, 7140, 166635, 3940755, 93771132,(2237012232), ...]; ...
coefficients in parenthesis form the initial terms of this sequence.
		

Programs

PARI

{a(n)=local(A=x,G=x+x^3); for(i=1,2*n-1, A=subst(G, x, A+x*O(x^(2*n)))); polcoeff(A, 2*n-1)}