A193099 E.g.f. A(x) satisfies: A'(x) = 1 + A(A(A(A(x)))).

1, 1, 4, 34, 466, 9044, 230827, 7388781, 287044354, 13212057907, 707417718215, 43431362340153, 3022050938855344, 236053437141340206, 20532456001485751429, 1975258248906891145913, 208928124926501980596761, 24172548454436633069025270

Offset

1,3

Links

Table of n, a(n) for n=1..18.

Example

 E.g.f.: A(x) = x + x^2/2! + 4*x^3/3! + 34*x^4/4! + 466*x^5/5! + 9044*x^6/6! +...
where the derivative of the e.g.f. begins:
A'(x) = 1 + x + 4*x^2/2! + 34*x^3/3! + 466*x^4/4! + 9044*x^5/5! +...
Related expansions.
A(A(x)) = x + 2*x^2/2! + 11*x^3/3! + 111*x^4/4! + 1702*x^5/5! + 35854*x^6/6! +...
A(A(A(x))) = x + 3*x^2/2! + 21*x^3/3! + 249*x^4/4! + 4303*x^5/5! + 99650*x^6/6! +...
A(A(A(A(x)))) = x + 4*x^2/2! + 34*x^3/3! + 466*x^4/4! + 9044*x^5/5! +...

Prog

 (PARI) {a(n)=local(A=x); for(i=1, n, A=intformal(1+subst(A, x, subst(A, x, subst(A, x, A+O(x^(n+1))))))); n!*polcoeff(A, n)}

Crossrefs

Cf. A001028, A193098, A193100, A179420.

Sequence in context: A218674 A321264 A234291 * A368445 A208831 A294475

Adjacent sequences: A193096 A193097 A193098 * A193100 A193101 A193102

Keyword

nonn

Author

Paul D. Hanna, Jul 15 2011

Status

approved