A270715 a(n) = ((n+2)/2)*Sum_{k=0..n/2}(Sum_{i=0..n-2*k} binomial(k+1,n-2*k-i)*binomial(k+i,k))/(k+1).
1, 3, 5, 10, 19, 35, 65, 120, 221, 407, 749, 1378, 2535, 4663, 8577, 15776, 29017, 53371, 98165, 180554, 332091, 610811, 1123457, 2066360, 3800629, 6990447, 12857437, 23648514, 43496399, 80002351, 147147265
Offset: 0
Keywords
Links
- Index entries for linear recurrences with constant coefficients, signature (2, 0, 0, -1).
Programs
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Mathematica
LinearRecurrence[{2,0,0,-1},{1,3,5,10},40] (* Harvey P. Dale, May 23 2017 *) -
Maxima
a(n):=(n+2)/2*(sum(sum(binomial(k+1,n-2*k-i)*binomial(k+i,k),i,0,n-2*k)/(k+1),k,0,n/2));
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PARI
x='x+O('x^200); Vec((-x^2+x+1)/((1-x)*(-x^3-x^2-x+1))) \\ Altug Alkan, Mar 22 2016
Formula
G.f.: (-x^2+x+1)/((1-x)*(-x^3-x^2-x+1)).