A180747 G.f.: A(x) = x/Series_Reversion(x*G(x)) where G(x) = Sum_{n>=0} (n+1)^(n-1)*x^n.

1, 1, 2, 9, 68, 715, 9527, 152789, 2856984, 60962112, 1461364051, 38885737209, 1137587558289, 36299474019445, 1254966476969859, 46739853740801293, 1865947811034153032, 79499993864122690971, 3600874278814894340648

Offset

0,3

Links

Paul D. Hanna, Table of n, a(n) for n = 0..300

Formula

G.f. satisfies: [x^n] A(x)^(n+1) = (n+1)^n for n>=0.

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

Example

G.f.: A(x) = 1 + x + 2*x^2 + 9*x^3 + 68*x^4 + 715*x^5 +...
G.f. satisfies A(x) = G(x/A(x)) where G(x) begins:
G(x) = 1 + x + 3*x^2 + 4^2*x^3 + 5^3*x^4 + 6^4*x^5 +...
so that:
A(x) = 1 + x/A(x) + 3*x^2/A(x)^2 + 4^2*x^3/A(x)^3 + 5^3*x^4/A(x)^4 +...
The coefficients in A(x)^n for n=1..8 begin:
A^1: [(1), 1, 2, 9, 68, 715, 9527, 152789, 2856984, ...];
A^2: [1,(2), 5, 22, 158, 1602, 20837, 328716, ...];
A^3: [1, 3,(9), 40, 276, 2700, 34250, 531093, ...];
A^4: [1, 4, 14,(64), 429, 4056, 50146, 763752, ...];
A^5: [1, 5, 20, 95,(625), 5726, 68975, 1031130,  ...];
A^6: [1, 6, 27, 134, 873,(7776), 91268, 1338366, ...];
A^7: [1, 7, 35, 182, 1183, 10283,(117649), 1691411, ...];
A^8: [1, 8, 44, 240, 1566, 13336, 148848,(2097152), ...]; ...
where the coefficient of x^n in A(x)^(n+1) equals (n+1)^n.

Prog

(PARI) {a(n)=polcoeff(x/serreverse(x*sum(m=0, n+1, (m+1)^(m-1)*x^m)+x^2*O(x^n)), n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A182957, A180749.

Sequence in context: A295239 A120020 A200248 * A227457 A134200 A217066

Adjacent sequences: A180744 A180745 A180746 * A180748 A180749 A180750

Keyword

nonn

Author

Paul D. Hanna, Jan 22 2011

Status

approved