A120957 Sequence uniquely defined by: n*a(n) = (n-1)*[x^n] B(x) for n>1 with a(0)=a(1)=1, or, equivalently, x*A'(x) = 1+x - B(x) + x*B'(x), where B(x) = series_reversion(x/A(x))/x.

1, 1, 1, 8, 123, 3024, 106850, 5110440, 317955435, 24986363648, 2422868732514, 284385893015080, 39758967921029830, 6530586385172586528, 1245479442254732687652, 272988926352496428778928

Offset

0,4

Comments

a(n) is divisible by (n-1) for n>1.

Links

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

Formula

The g.f. of A120958 equals B(x) = series_reversion(x/A(x))/x, so that both A(x) = B(x/A(x)) and B(x) = A(x*B(x)) equivalently hold.

Prog

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

Crossrefs

Sequence in context: A264408 A364985 A376099 * A302356 A367122 A069459

Adjacent sequences: A120954 A120955 A120956 * A120958 A120959 A120960

Keyword

nonn

Author

Paul D. Hanna, Jul 21 2006

Status

approved