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A110576
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Sequence is {a(0,n)}, where a(m,0)=1, a(m,n) = a(m,n-1) + a(m-1,n), a(0,n+1) = a(n,n).
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5
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1, 1, 2, 7, 29, 132, 648, 3407, 19109, 113946, 719896, 4802318, 33712717, 248285282, 1912928549, 15379305080, 128729241725, 1119519156562, 10097102345993, 94285391374568, 910145431036423, 9069616636456648, 93179779321299479
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OFFSET
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0,3
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COMMENTS
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Equals eigensequence of triangle A100100. - Gary W. Adamson, Feb 02 2009
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..570
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FORMULA
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a(0, n+1) = Sum_{k=0..n} binomial(2*n-k-1, n-1)*a(0, k), with a(0,0) =1.
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EXAMPLE
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a(0,n): 1,1,2,7,29
a(1,n): 1,2,4,11
a(2,n): 1,3,7,18
a(3,n): 1,4,11,29
Since a(3,3) = 29, a(0,4) also is 29.
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MATHEMATICA
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a[0, 0] := 1; a[0, 1] := 1; a[0, n_] := a[0, n] = Sum[Binomial[2*n - k - 3, n - 2]*a[0, k], {k, 0, n - 1}]; Table[a[0, n], {n, 0, 50}] (* G. C. Greubel, Aug 31 2017 *)
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CROSSREFS
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Cf. A110577, A110578, A110579, A110580.
Cf. A100100 [From Gary W. Adamson, Feb 02 2009]
Sequence in context: A007852 A300048 A232971 * A074600 A064641 A183608
Adjacent sequences: A110573 A110574 A110575 * A110577 A110578 A110579
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KEYWORD
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easy,nonn
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AUTHOR
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Leroy Quet, Jul 28 2005
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EXTENSIONS
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More terms from Ryan Propper, Sep 25 2005
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STATUS
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approved
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