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

0,2

Links

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (2, 0, 0, -1).

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

Cf. A113413, A270709.

Sequence in context: A320921 A084321 A323812 * A291735 A261050 A158943

Adjacent sequences: A270712 A270713 A270714 * A270716 A270717 A270718

Keyword

nonn

Author

Vladimir Kruchinin, Mar 22 2016

Status

approved