A177773 a(n) = [x^n] A_{n-1}(x)/n for n>2 where g.f. A(x) = Sum_{n>=1} a(n)*x^n and where A_{n+1}(x) = A_{n}(A(x)) denotes iteration with A_0(x)=x.

1, 1, 2, 39, 1808, 154470, 21613904, 4613731395, 1428023881948, 615891861903012, 358339956451941720, 273806861542425812854, 268629162417425144396676, 331966590301219201136933748, 508293097203298105978769282272

Offset

1,3

Links

Table of n, a(n) for n=1..15.

Example

G.f.: A(x) = x + x^2 + 2*x^3 + 39*x^4 + 1808*x^5 + 154470*x^6 +...
Coefficients in the initial iterations of A(x) begin:
[1, 1, 2, 39, 1808, 154470, 21613904, 4613731395,...];
[1, 2,(6), 89, 3872, 322484, 44522028, 9428171190,...];
[1, 3, 12,(156), 6254, 505736, 68824132, 14453842282,...];
[1, 4, 20, 246,(9040), 706314, 94632484, 19702073310,...];
[1, 5, 30, 365, 12340,(926820), 122074704, 25185102729,...];
[1, 6, 42, 519, 16288, 1170490,(151297328), 30916206032,...];
[1, 7, 56, 714, 21042, 1441314, 182470092,(36909851160),...];
[1, 8, 72, 956, 26784, 1744156, 215790936, 43181887140, (12852214937532), ...]; ...
where the above terms in parenthesis illustrate the property
that the coefficient of x^n in A_{n-1}(x) = n*a(n):
6 = 3*2; 156 = 4*39; 9040 = 5*1808; 926820 = 6*154470; ...

Prog

(PARI) {a(n)=local(F=x+x^2+sum(m=3, n-1, a(m)*x^m)+x*O(x^n), G=x); for(i=1, n-1, G=subst(G, x, F)); if(n<1, 0, if(n<3, 1, polcoeff(G, n)))}

Crossrefs

Sequence in context: A266863 A245053 A352021 * A274574 A212615 A247878

Adjacent sequences: A177770 A177771 A177772 * A177774 A177775 A177776

Keyword

nonn

Author

Paul D. Hanna, May 13 2010

Status

approved