A179501 Logarithmic derivative of A179500.

1, 3, 10, 43, 276, 3138, 80998, 7043187, 3719589796, 27895892650378, 9982024484486217164, 953757232905143490078932902, 293418537539006210065580840496997061594

Offset

1,2

Comments

The g.f. of A179500, G(x), is defined by:

. G(x) = exp( Sum_{n>=1} [Sum_{k>=0} A179500(k)^n* x^k]^n* x^n/n );

the g.f. of this sequence is L(x) = log(G(x)).

Links

Table of n, a(n) for n=1..13.

Example

L.g.f.: L(x) = x + 3*x^2/2 + 10*x^3/3 + 43*x^4/4 + 276*x^5/5 +...
The g.f. of A179500, G(x) = exp(L(x)), begins:
G(x) = 1 + x + 2*x^2 + 5*x^3 + 16*x^4 + 74*x^5 + 612*x^6 + 12271*x^7+...
where L(x) = log(G(x)) equals the series:
L(x) = (1 + x + 2*x^2 + 5*x^3 + 16*x^4 + 74*x^5 +...)*x
+ (1 + x + 2^2*x^2 + 5^2*x^3 + 16^2*x^4 + 74^2*x^5 +...)^2*x^2/2
+ (1 + x + 2^3*x^2 + 5^3*x^3 + 16^3*x^4 + 74^3*x^5 +...)^3*x^3/3
+ (1 + x + 2^4*x^2 + 5^4*x^3 + 16^4*x^4 + 74^4*x^5 +...)^4*x^4/4
+ (1 + x + 2^5*x^2 + 5^5*x^3 + 16^5*x^4 + 74^5*x^5 +...)^5*x^5/5 +...

Prog

(PARI) {a(n)=local(L, G, A179500); G=exp(x+sum(k=2, n-1, a(k)*x^k/k)+x*O(x^n)); A179500=Vec(G); L=sum(m=1, n, sum(k=0, n-m, A179500[k+1]^m*x^k+x*O(x^n))^m*x^m/m); n*polcoeff(L, n)}

Crossrefs

Cf. A179501.

Sequence in context: A181949 A162286 A032269 * A041737 A279105 A246956

Adjacent sequences: A179498 A179499 A179500 * A179502 A179503 A179504

Keyword

nonn

Author

Paul D. Hanna, Sep 21 2010

Status

approved