A191586 Binomial row sums of the Riordan matrix (1/(1-x),x/(1-x^2)) (A046854).

1, 2, 4, 11, 32, 92, 271, 814, 2464, 7508, 23024, 70952, 219503, 681358, 2121116, 6619571, 20703040, 64873328, 203625604, 640109128, 2014951552, 6350490808, 20037015200, 63284778256, 200063948527, 633007850942, 2004431426716, 6351693835169, 20141013776384

Offset: 0

Author

Emanuele Munarini, Jun 07 2011

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..198

Crossrefs

Cf. A046854.

Programs

Mathematica

Table[Sum[Binomial[n, k]Binomial[Floor[(n+k)/2],k],{k,0,n}],{n,0,100}]

Maxima

makelist(sum(binomial(n,k)*binomial(floor((n+k)/2),k),k,0,n),n,0,12);

Formula

a(n) = Sum_{k=0..n} binomial(n,k)*binomial(floor((n+k)/2),k).

(8*n^2+88*n+240)*a(n+6) - (72*n^2+636*n+1380)*a(n+5) + (180*n^2+1300*n+2232)*a(n+4) - (180*n^2+1170*n+1842)*a(n+3) + (326*n^2+2074*n+3164)*a(n+2) - (228*n^2+948*n+984)*a(n+1) + (35*n^2+105*n+70)*a(n) = 0. - Emanuele Munarini, Aug 31 2017