OFFSET
0,2
FORMULA
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).
E.g.f.: (1+t)*exp(t+t^2+t^3/3).
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.
MATHEMATICA
AList[n_] := CoefficientList[Series[(1 + t) E^(t + t^2 + t^3/3), {t, 0, n}], t] Table[k!, {k, 0, n}]
AList[100]
PROG
(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);
makelist(a(n), n, 0, 24);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emanuele Munarini, Oct 20 2014
STATUS
approved