A110167 Diagonal sums of Riordan array A110165.
1, 3, 12, 51, 226, 1026, 4733, 22083, 103914, 492228, 2344035, 11211210, 53817063, 259135299, 1251074772, 6053946531, 29354128498, 142584834924, 693691007267, 3379680991356, 16486985580693, 80521218046569, 393674826425462
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
Programs
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Mathematica
Table[Sum[Sum[Binomial[n-k,j]*Binomial[2j,j+k],{j,0,n-k}],{k,0,Floor[n/2]}],{n,0,20}] (* Vaclav Kotesovec, Oct 18 2012 *)
Formula
G.f.: 2/sqrt(1-6*x+5*x^2)/(1+3*x+sqrt(1-6*x+5*x^2)).
a(n) = sum{k=0..floor(n/2), sum{j=0..n-k, C(n-k, j)*C(2*j, j+k)}}.
Recurrence: 3*(n+1)*(16*n-7)*a(n) = (272*n^2 + 9*n - 119)*a(n-1) - 3*(48*n^2 - 37*n - 31)*a(n-2) - 5*(n-1)*(16*n+9)*a(n-3). - Vaclav Kotesovec, Oct 18 2012
a(n) ~ 5^(n+3/2)/(8*sqrt(Pi*n)). - Vaclav Kotesovec, Oct 18 2012