A188460 Diagonal sums of number triangle A119308.
1, 2, 4, 9, 20, 45, 103, 238, 555, 1305, 3090, 7362, 17637, 42460, 102670, 249246, 607256, 1484343, 3639094, 8946260, 22048771, 54467577, 134842844, 334493154, 831296965, 2069573632, 5160747114, 12888640503, 32234749938, 80728619175, 202433907465
Offset: 0
Programs
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PARI
x='x+O('x^66); Vec((1-2*x-x^3-(1-x)*sqrt((x^2-3*x+1)*(x^2+x+1)))/(2*x^5)) \\ Joerg Arndt, May 11 2013
Formula
a(n)=sum{k=0..floor(n/2), sum{j=0..n-k, C(n-k,j)*if(k<=j, C(j+1,2*(j-k))*A000108(j-k),0)}}.
G.f.: (1-2*x-x^3-(1-x)*sqrt((x^2-3*x+1)*(x^2+x+1)))/(2*x^5). - Mark van Hoeij, May 10 2013
Conjecture: (n+5)*(n+1)*a(n) -(2*n+5)*(n+2)*a(n-1) -(n+2)*(n+1)*a(n-2) -(n+1)*(2*n+1)*a(n-3) +(n-2)*(n+2)*a(n-4)=0. - R. J. Mathar, Feb 13 2015
Comments