A205501 G.f. satisfies: A(x) = exp( Sum_{n>=1} x^n/n * Product_{d|n} A(d*x^d)^n ).

1, 1, 2, 5, 16, 50, 177, 608, 2205, 7948, 29552, 109554, 414342, 1568627, 6011290, 23102857, 89512855, 347930789, 1360252177, 5334715764, 21012372520, 83004307780, 328996301835, 1307386952248, 5209629950774, 20806467497993, 83287927579183, 334066903101026

Offset

0,3

Links

Table of n, a(n) for n=0..27.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 16*x^4 + 50*x^5 + 177*x^6 + 608*x^7 +...
By definition:
log(A(x)) = x*A(x) + x^2*A(x)^2*A(2*x^2)^2/2 + x^3*A(x)^3*A(3*x^3)^3/3 + x^4*A(x)^4*A(2*x^2)^4*A(4*x^4)^4/4 + x^5*A(x)^5*A(5*x^5)^5/5 + x^6*A(x)^6*A(2*x^2)^6*A(3*x^3)^6*A(6*x^6)^6/6 +...
Explicitly,
log(A(x)) = x + 3*x^2/2 + 10*x^3/3 + 43*x^4/4 + 156*x^5/5 + 672*x^6/6 + 2570*x^7/7 + 10619*x^8/8 + 41968*x^9/9 +...

Prog

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

Crossrefs

Cf. A205498, A205499, A205500, A205502.

Sequence in context: A148383 A148384 A148385 * A118973 A148386 A148387

Adjacent sequences: A205498 A205499 A205500 * A205502 A205503 A205504

Keyword

nonn

Author

Paul D. Hanna, Jan 27 2012

Status

approved