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A179500 G.f.: A(x) = exp( Sum_{n>=1} [Sum_{k>=0} a(k)^n* x^k]^n* x^n/n ). 2
1, 1, 2, 5, 16, 74, 612, 12271, 893422, 414194958, 2790004382642, 907459561737399050, 79479770316224310083608800, 22570656733849188237806831031463922346 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Paul D. Hanna, Table of n, a(n), n = 0..20.

EXAMPLE

G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 16*x^4 + 74*x^5 + 612*x^6 +...

The logarithm (A179501) begins:

log(A(x)) = x + 3*x^2/2 + 10*x^3/3 + 43*x^4/4 + 276*x^5/5 + 3138*x^6/6 + 80998*x^7/7 + 7043187*x^8/8 + 3719589796*x^9/9 +...

and equals the series:

log(A(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 +...

More explicitly,

log(A(x)) = (1 + x + 2*x^2 + 5*x^3 + 16*x^4 + 74*x^5 +...)*x

+ (1 + 2*x + 9*x^2 + 58*x^3 + 578*x^4 + 11664*x^5 +...)*x^2/2

+ (1 + 3*x + 27*x^2 + 424*x^3 + 13254*x^4 +...)*x^3/3

+ (1 + 4*x + 70*x^2 + 2696*x^3 + 271373*x^4 +...)*x^4/4

+ (1 + 5*x + 170*x^2 + 16275*x^3 + 5316585*x^4 +...)*x^5/5 +...

PROG

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

CROSSREFS

Cf. A179501.

Sequence in context: A078639 A002632 A020127 * A121396 A263914 A218168

Adjacent sequences:  A179497 A179498 A179499 * A179501 A179502 A179503

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 21 2010

STATUS

approved

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Last modified December 11 13:57 EST 2017. Contains 295877 sequences.