A120958 Sequence uniquely defined by: (n-1)*a(n) = n*[x^n] B(x) for n>1 with a(0)=a(1)=1, or, equivalently, 1+x - A(x) + x*A'(x) = x*B'(x), where B(x) = x/series_reversion(x*A(x)).

1, 1, 2, 12, 164, 3780, 128220, 5962180, 363377640, 28109659104, 2692076369460, 312824482316588, 43373419550214360, 7074801917270302072, 1341285553197404432856, 292488135377674745120280

Offset

0,3

Comments

a(n) is divisible by n for n>0.

Links

Table of n, a(n) for n=0..15.

Formula

The g.f. of A120957 equals B(x) = x/series_reversion(x*A(x)), so that both A(x) = B(x*A(x)) and B(x) = A(x/B(x)) equivalently hold.

Prog

(PARI) {a(n)=my(A=[1, 1]); if(n==0||n==1, 1, for(i=1, n, A=concat(A, 0); A[ #A]=(#A-2)*Vec(serreverse(x/Ser(A)))[ #A]); A[n+1]*n/(n-1))}

Crossrefs

Sequence in context: A302688 A201007 A226058 * A030163 A368981 A255163

Adjacent sequences: A120955 A120956 A120957 * A120959 A120960 A120961

Keyword

nonn

Author

Paul D. Hanna, Jul 21 2006

Status

approved