A199102 G.f. satisfies: A(x) = exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} C(n,k)*A(x^(n+k)) ).

1, 2, 6, 20, 63, 213, 719, 2505, 8864, 31948, 116725, 432074, 1616022, 6100775, 23214144, 88949045, 342899474, 1329020016, 5175758820, 20243197030, 79480515302, 313155710230, 1237771800135, 4906616164195, 19502048947616, 77703941363599, 310305199056779

Offset

0,2

Links

Table of n, a(n) for n=0..26.

Example

G.f.: A(x) = 1 + 2*x + 6*x^2 + 20*x^3 + 63*x^4 + 213*x^5 + 719*x^6 +...
where
log(A(x)) = (A(x)+A(x^2))*x + (A(x^2)+2*A(x^3)+A(x^4))*x^2/2 + (A(x^3)+3*A(x^4)+3*A(x^5)+A(x^6))*x^3/3 + (A(x^4)+4*A(x^5)+6*A(x^6)+4*A(x^7)+A(x^8))*x^4/4 +...
Explicitly,
log(A(x)) = 2*x + 8*x^2/2 + 32*x^3/3 + 100*x^4/4 + 387*x^5/5 + 1370*x^6/6 + 5315*x^7/7 + 20444*x^8/8 + 80897*x^9/9 + 320883*x^10/10 +...

Prog

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

Crossrefs

Cf. A073063.

Sequence in context: A247076 A177792 A193235 * A053730 A220874 A273902

Adjacent sequences: A199099 A199100 A199101 * A199103 A199104 A199105

Keyword

nonn

Author

Paul D. Hanna, Nov 03 2011

Status

approved