The On-Line Encyclopedia of Integer Sequences (OEIS)

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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.
(history; published version)

#6 by Russ Cox at Fri Mar 30 16:49:31 EDT 2012

AUTHOR

_N. J. A. Sloane (njas(AT)research.att.com), _, Oct 29 2002

Discussion

Fri Mar 30

16:49

OEIS Server: https://oeis.org/edit/global/110

#5 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

KEYWORD

nonn,tabl,new

AUTHOR

N. J. A. Sloane (njas, (AT)research.att.com), Oct 29 2002

#4 by N. J. A. Sloane at Tue Jan 24 03:00:00 EST 2006

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)

KEYWORD

nonn,tabl,new

#3 by N. J. A. Sloane at Sun Feb 20 03:00:00 EST 2005

DATA

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

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)

KEYWORD

nonn,tabl,more,new

EXTENSIONS

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

#2 by N. J. A. Sloane at Wed Sep 22 03:00:00 EDT 2004

NAME

Square array read by anti-diagonals 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.

KEYWORD

nonn,tabl,more,new

#1 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003

NAME

Square array by anti-diagonals 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.

DATA

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

OFFSET

0,9

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 ...

CROSSREFS

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

KEYWORD

nonn,tabl,more

AUTHOR

njas, Oct 29 2002

STATUS

approved