A076037 Square array read by antidiagonals in which row n has g.f. (1-(n-1)*x*C)/(1-n*x*C) where C = (1/2-1/2*(1-4*x)^(1/2))/x = g.f. for Catalan numbers A000108.

1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 5, 5, 1, 1, 4, 10, 14, 14, 1, 1, 5, 17, 35, 42, 42, 1, 1, 6, 26, 74, 126, 132, 132, 1, 1, 7, 37, 137, 326, 462, 429, 429, 1, 1, 8, 50, 230, 726, 1446, 1716, 1430, 1430, 1, 1, 9, 65, 359, 1434, 3858, 6441, 6435, 4862, 4862, 1, 1, 10, 82

Offset: 0

Author

N. J. A. Sloane, Oct 29 2002

Keywords

• nonn
• tabl

Examples

			Array begins
1 1 1 2 5 14 42 ... (n=0)
1 1 2 5 14 42 132 ... (n=1)
1 1 3 10 35 126 ... (n=2)
1 1 4 17 74 326 ...
		

Crossrefs

Rows give A000108, A000108, A001700, A049027, A076025, A076026. Cf. A076038, A067347.

Programs

PARI

C(x)=(1/2-1/2*(1-4*x)^(1/2))/x; D(x)=(1-(m-1)*x*C(x))/(1-m*x*C(x)); for(i=0,15, forstep(m=i,0,-1,print1(polcoeff(D(x),i-m),","));print()) (Klasen)

Extensions

More terms from Lambert Klasen (lambert.klasen(AT)gmx.de), Jan 12 2005