A108478 - OEIS

%I #12 Sep 27 2014 19:05:46

%S 1,1,2,14,43,127,468,1596,5253,17917,60918,205194,694287,2351611,

%T 7951336,26894840,91004105,307854073,1041410602,3523170438,

%U 11918842803,40320750711,136404504124,461454010164,1561085306061,5281113937653

%N Diagonal sums of number triangle A108477.

%F a(n) = sum_{k=0..floor(n/2)} ( sum_{j=0..n-k} C(2(n-2k), j)*C(2k, j)*2^j ).

%F Empirical g.f.: -(3*x^3+x^2+x-1) / ((x^3-3*x^2-x-1)*(x^3+x^2+3*x-1)). - _Colin Barker_, Sep 26 2014

%p A108478:=n->add(add(binomial(2*(n-2*k),j)*binomial(2*k,j)*2^j, j=0..n-k), k=0..floor(n/2)): seq(A108478(n), n=0..30); # _Wesley Ivan Hurt_, Sep 26 2014

%t Table[Sum[Sum[Binomial[2 (n - 2 k), j]*Binomial[2 k, j]*2^j, {j, 0, n - k}], {k, 0, Floor[n/2]}], {n, 0, 30}] (* _Wesley Ivan Hurt_, Sep 26 2014 *)

%o (PARI) a(n) = sum(k=0, n\2, sum(j=0, n-k, binomial(2*(n-2*k), j)*binomial(2*k, j)*2^j)); \\ _Michel Marcus_, Sep 26 2014

%K easy,nonn

%O 0,3

%A _Paul Barry_, Jun 04 2005