A193353 G.f. satisfies: A(x) = Sum_{n>=0} x^n * Product_{k=1..n} A(k*x)/(1+k*x).

1, 1, 1, 2, 7, 30, 197, 1770, 22536, 409456, 10541949, 387914810, 20362048664, 1525681168956, 163330533908217, 24973901010606886, 5456672750531017964, 1704092792275195175172, 760753610853139920737328, 485646261179496433286709024

Offset

0,4

Links

Table of n, a(n) for n=0..19.

Example

G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 7*x^4 + 30*x^5 + 197*x^6 + 1770*x^7 +...
where
A(x) = 1 + x*A(x)/(1+x) + x^2*A(x)*A(2*x)/((1+x)*(1+2*x)) + x^3*A(x)*A(2*x)*A(3*x)/((1+x)*(1+2*x)*(1+3*x)) +...

Prog

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

Crossrefs

Sequence in context: A020045 A020135 A249474 * A391000 A102158 A380333

Adjacent sequences: A193350 A193351 A193352 * A193354 A193355 A193356

Keyword

nonn

Author

Paul D. Hanna, Jul 23 2011

Status

approved