A110576 - OEIS

%I #17 Jun 05 2021 15:24:12

%S 1,1,2,7,29,132,648,3407,19109,113946,719896,4802318,33712717,

%T 248285282,1912928549,15379305080,128729241725,1119519156562,

%U 10097102345993,94285391374568,910145431036423,9069616636456648,93179779321299479

%N 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).

%C Equals eigensequence of triangle A100100. - _Gary W. Adamson_, Feb 02 2009

%H G. C. Greubel, <a href="/A110576/b110576.txt">Table of n, a(n) for n = 0..570</a>

%F a(0, n+1) = Sum_{k=0..n} binomial(2*n-k-1, n-1)*a(0, k), with a(0,0) = 1.

%e a(0,n): 1, 1, 2, 7, 29

%e a(1,n): 1, 2, 4, 11

%e a(2,n): 1, 3, 7, 18

%e a(3,n): 1, 4, 11, 29

%e Since a(3,3) = 29, a(0,4) also is 29.

%t 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 *)

%Y Cf. A110577, A110578, A110579, A110580.

%Y Cf. A100100. - _Gary W. Adamson_, Feb 02 2009

%K easy,nonn

%O 0,3

%A _Leroy Quet_, Jul 28 2005

%E More terms from _Ryan Propper_, Sep 25 2005