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Search: id:A076038
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| A076038 |
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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. |
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+0
2
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| 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; listen)
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OFFSET
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0,5
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FORMULA
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a(n, m) = 1/(m+1)*Sum_{k=0..m} binomial(2*m-k, m)*(k+1)*(n-m)^k, m=0..n.
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EXAMPLE
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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 ...
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CROSSREFS
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Rows give A000108, A000108, A001700, A049027, A076025, A076026. Cf. A076037, A067347.
Cf. A059718.
Sequence in context: A064580 A009766 A059718 this_sequence A095788 A071944 A080955
Adjacent sequences: A076035 A076036 A076037 this_sequence A076039 A076040 A076041
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KEYWORD
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nonn,tabl
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Oct 29 2002
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 18 2003
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