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

0,2

Links

Table of n, a(n) for n=0..23.

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

Cf. A049425.

Sequence in context: A308241 A363061 A288910 * A322555 A118814 A345878

Adjacent sequences: A249059 A249060 A249061 * A249063 A249064 A249065

Keyword

nonn

Author

Emanuele Munarini, Oct 20 2014

Status

approved