A076037 - OEIS

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

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OFFSET

0,9

LINKS

Table of n, a(n) for n=0..69.

EXAMPLE

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 ...

PROG

(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)

CROSSREFS

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

Sequence in context: A290252 A336706 A344567 * A215563 A076263 A272689

Adjacent sequences: A076034 A076035 A076036 * A076038 A076039 A076040

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Oct 29 2002

EXTENSIONS

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

STATUS

approved