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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
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
0,2
FORMULA
G.f.: (-x^2+x+1)/((1-x)*(-x^3-x^2-x+1)).
MATHEMATICA
LinearRecurrence[{2, 0, 0, -1}, {1, 3, 5, 10}, 40] (* Harvey P. Dale, May 23 2017 *)
PROG
(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));
(PARI) x='x+O('x^200); Vec((-x^2+x+1)/((1-x)*(-x^3-x^2-x+1))) \\ Altug Alkan, Mar 22 2016
CROSSREFS
Sequence in context: A320921 A084321 A323812 * A291735 A261050 A158943
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Mar 22 2016
STATUS
approved