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A110576
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).
5
1, 1, 2, 7, 29, 132, 648, 3407, 19109, 113946, 719896, 4802318, 33712717, 248285282, 1912928549, 15379305080, 128729241725, 1119519156562, 10097102345993, 94285391374568, 910145431036423, 9069616636456648, 93179779321299479
OFFSET
0,3
COMMENTS
Equals eigensequence of triangle A100100. - Gary W. Adamson, Feb 02 2009
LINKS
FORMULA
a(0, n+1) = Sum_{k=0..n} binomial(2*n-k-1, n-1)*a(0, k), with a(0,0) = 1.
EXAMPLE
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.
MATHEMATICA
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 *)
CROSSREFS
Cf. A100100. - Gary W. Adamson, Feb 02 2009
Sequence in context: A232971 A366084 A368935 * A074600 A064641 A183608
KEYWORD
easy,nonn
AUTHOR
Leroy Quet, Jul 28 2005
EXTENSIONS
More terms from Ryan Propper, Sep 25 2005
STATUS
approved