|
|
A161967
|
|
E.g.f. satisfies: A(x) = exp( x*exp( x*A'(x)/A(x) ) ), where A'(x)/A(x) = d/dx log(A(x)).
|
|
3
|
|
|
1, 1, 3, 22, 317, 7596, 270727, 13332544, 862740153, 70762448080, 7161344443691, 875732817920544, 127244974218410677, 21666397760623131712, 4273075677258426773295, 966395699152796722817536
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
EXAMPLE
|
E.g.f.: A(x) = 1 + x + 3*x^2/2! + 22*x^3/3! + 317*x^4/4! + 7596*x^5/5! +...
A'(x)/A(x) = 1 + 2*x + 15*x^2/2! + 232*x^3/3! + 5905*x^4/4! + 220176*x^5/5! +...
where x*exp( x*d/dx log(A(x)) ) = log(A(x)) = e.g.f. of A161968.
|
|
PROG
|
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(x*exp(x*deriv(A)/(A+O(x^n))))); n!*polcoeff(A, n)}
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|