[seqfan] Re: A137777 starts with a gap

Peter Luschny peter.luschny at googlemail.com
Tue Apr 21 21:32:49 CEST 2009

> Table[CoefficientList[2 BernoulliB[k,x] Gamma[2+k],x],{k,0,10}]//Flatten

Roger L. Bagula said that g := (x,t) -> t^2*exp(x*t)/(exp(t)-1)
is not the generating function of the Bernoulli polynomials.
This is true, of course.

So I am stuck. But not satisfied. Perhaps I will shorten your
solution. Since I can not find a pair of '()' to eliminate I will
eliminate the '2'. This number looks quiet arbitrary here to me.

T := Table[CoefficientList[BernoulliB[k,x] Gamma[2+k],x],{k,0,10}]//Flatten

Additional advantage are the cleaner
T(n,0) = A129814(n) for n >= 0;
T(n,n) = (n+1)!     for n >= 0.

But I have to rethink this after I have studied A159749
(somewhere in the OEIS queue) .

Cheers Peter

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