cp's OEIS Frontend

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

%I A180747 #10 Jan 22 2018 10:58:14
%S A180747 1,1,2,9,68,715,9527,152789,2856984,60962112,1461364051,38885737209,
%T A180747 1137587558289,36299474019445,1254966476969859,46739853740801293,
%U A180747 1865947811034153032,79499993864122690971,3600874278814894340648
%N A180747 G.f.: A(x) = x/Series_Reversion(x*G(x)) where G(x) = Sum_{n>=0} (n+1)^(n-1)*x^n.
%H A180747 Paul D. Hanna, <a href="/A180747/b180747.txt">Table of n, a(n) for n = 0..300</a>
%F A180747 G.f. satisfies: [x^n] A(x)^(n+1) = (n+1)^n for n>=0.
%F A180747 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.
%e A180747 G.f.: A(x) = 1 + x + 2*x^2 + 9*x^3 + 68*x^4 + 715*x^5 +...
%e A180747 G.f. satisfies A(x) = G(x/A(x)) where G(x) begins:
%e A180747 G(x) = 1 + x + 3*x^2 + 4^2*x^3 + 5^3*x^4 + 6^4*x^5 +...
%e A180747 so that:
%e A180747 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 +...
%e A180747 The coefficients in A(x)^n for n=1..8 begin:
%e A180747 A^1: [(1), 1, 2, 9, 68, 715, 9527, 152789, 2856984, ...];
%e A180747 A^2: [1,(2), 5, 22, 158, 1602, 20837, 328716, ...];
%e A180747 A^3: [1, 3,(9), 40, 276, 2700, 34250, 531093, ...];
%e A180747 A^4: [1, 4, 14,(64), 429, 4056, 50146, 763752, ...];
%e A180747 A^5: [1, 5, 20, 95,(625), 5726, 68975, 1031130,  ...];
%e A180747 A^6: [1, 6, 27, 134, 873,(7776), 91268, 1338366, ...];
%e A180747 A^7: [1, 7, 35, 182, 1183, 10283,(117649), 1691411, ...];
%e A180747 A^8: [1, 8, 44, 240, 1566, 13336, 148848,(2097152), ...]; ...
%e A180747 where the coefficient of x^n in A(x)^(n+1) equals (n+1)^n.
%o A180747 (PARI) {a(n)=polcoeff(x/serreverse(x*sum(m=0,n+1,(m+1)^(m-1)*x^m)+x^2*O(x^n)),n)}
%o A180747 for(n=0,20,print1(a(n),", "))
%Y A180747 Cf. A182957, A180749.
%K A180747 nonn
%O A180747 0,3
%A A180747 _Paul D. Hanna_, Jan 22 2011