A222012 G.f. satisfies: A(x) = Sum_{n>=0} n^n * x^n * A(x)^n / (1 + n*x*A(x))^n.

1, 1, 4, 22, 145, 1081, 8863, 78751, 752587, 7708483, 84532222, 992628616, 12487788067, 168344145919, 2430351826084, 37517872149790, 617842147959019, 10821864145358779, 200955801421862020, 3943205940005194330, 81506338541922078355, 1769606318933022398611

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

G.f. satisfies: A(x) = 1 + Sum_{n>=1} (n+1)!/2 * x^n * A(x)^n.

G.f.: (1/x)*Series_Reversion(x/B(x)), where B(x) = 1 + Sum_{n>=1} (n+1)!/2*x^n.

Example

G.f.: A(x) = 1 + x + 4*x^2 + 22*x^3 + 145*x^4 + 1081*x^5 + 8863*x^6 +...
where, by definition,
A(x) = 1 + x*A(x)/(1+x*A(x)) + 2^2*x^2*A(x)^2/(1+2*x*A(x))^2 + 3^3*x^3*A(x)^3/(1+3*x*A(x))^3 + 4^4*x^4*A(x)^4/(1+4*x*A(x))^4 +....
also, g.f. A(x) satisfies:
A(x) = 1 + x*A(x) + 3*x^2*A(x)^2 + 12*x^3*A(x)^3 + 60*x^4*A(x)^4 + 360*x^5*A(x)^5 + 2520*x^6*A(x)^6 +...+ (n+1)!/2*x^n*A(x)^n +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, m^m*x^m*A^m/(1+m*x*A+x*O(x^n))^m)); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
(PARI) {a(n)=local(B=1+sum(m=1, n, (m+1)!/2*x^m)+x*O(x^n)); polcoeff(1/x*serreverse(x/B), n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A211207.

Sequence in context: A027391 A134988 A081002 * A057834 A196795 A278396

Adjacent sequences: A222009 A222010 A222011 * A222013 A222014 A222015

Keyword

nonn

Author

Paul D. Hanna, Feb 04 2013

Status

approved