A222034 G.f. satisfies: A(x) = Sum_{n>=0} n! * x^n * Product_{k=1..n} A(k*x)/(1 + k*x*A(k*x)).

1, 1, 2, 7, 38, 302, 3428, 55083, 1251590, 40289986, 1841412556, 119672298150, 11071253179356, 1459246211179612, 274215745471606536, 73511068056751643571, 28128768433558172885958, 15371204139970896651788090, 12001328910786418412379456956

Offset

0,3

Comments

Compare to the identity: 1/(1-x) = Sum_{n>=0} n!*x^n/Product_{k=1..n} (1+k*x).

Links

Table of n, a(n) for n=0..18.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 38*x^4 + 302*x^5 + 3428*x^6 +...
where, by definition,
A(x) = 1 + x*A(x)/(1+x*A(x)) + 2!*x^2*A(x)*A(2*x)/((1+x*A(x))*(1+2*x*A(2*x))) + 3!*x^3*A(x)*A(2*x)*A(3*x)/((1+x*A(x))*(1+2*x*A(2*x))*(1+3*x*A(3*x))) + 4!*x^4*A(x)*A(2*x)*A(3*x)*A(4*x)/((1+x*A(x))*(1+2*x*A(2*x))*(1+3*x*A(3*x))*(1+4*x*A(4*x))) +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, m!*x^m*prod(k=1, m, subst(A, x, k*x+x*O(x^n ))/(1+k*x*subst(A, x, k*x+x*O(x^n)))))); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A000366 A341381 A106211 * A337685 A014058 A119602

Adjacent sequences: A222031 A222032 A222033 * A222035 A222036 A222037

Keyword

nonn

Author

Paul D. Hanna, Feb 06 2013

Status

approved