A249062 - OEIS

%I #7 Oct 21 2014 04:09:44

%S 1,2,5,18,69,306,1497,7890,45033,273474,1760301,11961522,85265325,

%T 636026418,4947725889,40019230386,335868650577,2918173355010,

%U 26199114476373,242657102748114,2314964975130261,22717352863875762,229029972003647145,2369438933865972498

%N A double binomial sum.

%F a(n) = sum((n!/k!)*sum(bin(k,i)*bin(k-i+1,n-k-2*i)/3^i,i=0..k),k=0..n).

%F E.g.f.: (1+t)*exp(t+t^2+t^3/3).

%F a(n+4)+(n+1)*a(n+3)-3*(n+3)*a(n+2)-3*(n+3)*(n+2)*a(n+1)-(n+3)*(n+2)*(n+1)*a(n)=0.

%t AList[n_] := CoefficientList[Series[(1 + t) E^(t + t^2 + t^3/3), {t, 0, n}], t] Table[k!, {k, 0, n}]

%t AList[100]

%o (Maxima) a(n) := sum((n!/k!)*sum(binomial(k,i)*binomial(k-i+1,n-k-2*i)/3^i,i,0,k),k,0,n);

%o makelist(a(n),n,0,24);

%Y Cf. A049425.

%K nonn

%O 0,2

%A _Emanuele Munarini_, Oct 20 2014