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A076038 Square array read by antidiagonals in which row n has g.f. 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, 2, 2, 1, 3, 5, 5, 1, 4, 10, 14, 14, 1, 5, 17, 35, 42, 42, 1, 6, 26, 74, 126, 132, 132, 1, 7, 37, 137, 326, 462, 429, 429, 1, 8, 50, 230, 726, 1446, 1716, 1430, 1430, 1, 9, 65, 359, 1434, 3858, 6441, 6435, 4862, 4862, 1, 10, 82, 530, 2582, 8952, 20532, 28770 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..62.

FORMULA

a(n, m) = 1/(m+1)*Sum_{k=0..m} binomial(2*m-k, m)*(k+1)*(n-m)^k, m=0..n.

EXAMPLE

Array begins

1 1 2 5 14 42 ... (n=0)

1 2 5 14 42 132 ... (n=1)

1 3 10 35 126 ... (n=2)

1 4 17 74 326 ...

CROSSREFS

Rows give A000108, A000108, A001700, A049027, A076025, A076026. Cf. A076037, A067347.

Cf. A059718.

Sequence in context: A064580 A009766 A059718 * A095788 A071944 A080955

Adjacent sequences:  A076035 A076036 A076037 * A076039 A076040 A076041

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Oct 29 2002

EXTENSIONS

More terms from Vladeta Jovovic, Jul 18 2003

STATUS

approved

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Last modified October 20 18:08 EDT 2018. Contains 316401 sequences. (Running on oeis4.)