A138912 - OEIS

%I #2 Mar 30 2012 18:37:10

%S 1,1,2,9,28,145,726,4249,27000,186561,1387450,11034001,93295236,

%T 834720913,7870851366,77943848025,808159323376,8749874083585,

%U 98687599614450,1157060036429857,14075106913366140,177337182574590801

%N Inverse binomial transform of A138911.

%C The n-th term of the n-th inverse binomial transform of A138911 is 1 for n>=0.

%F O.g.f. satisfies: [x^n] A( x/(1+(n-1)*x) )/(1+(n-1)*x) = 1 for n>=0.

%F E.g.f. satisfies: [x^n] A(x)*exp(-(n-1)*x) = 1/n! for n>=0.

%o (PARI) {a(n)=local(A=[1]);for(k=1,n,A=concat(A,0); A[k+1]=1-polcoeff(subst(Ser(A),x,x/(1+(k-1)*x+x*O(x^k)))/(1+(k-1)*x),k));A[n+1]}

%Y Cf. A138911 (binomial transform).

%K nonn

%O 0,3

%A _Paul D. Hanna_, Apr 05 2008