A249062 A double binomial sum.

1, 2, 5, 18, 69, 306, 1497, 7890, 45033, 273474, 1760301, 11961522, 85265325, 636026418, 4947725889, 40019230386, 335868650577, 2918173355010, 26199114476373, 242657102748114, 2314964975130261, 22717352863875762, 229029972003647145, 2369438933865972498

Offset: 0

Author

Emanuele Munarini, Oct 20 2014

Keywords

• nonn

Crossrefs

Cf. A049425.

Programs

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]

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);

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.