A306087 - OEIS

%I #12 Jun 23 2018 22:51:11

%S -1,1,-1,-2,8,56,-281,-3061,18612,271129,-1925781,-34967550,284063311,

%T 6174304311,-56535769915,-1431894779510,14610783773266,

%U 422789237646634,-4761801655073506,-155050750819877478,1911855043475987609,69202778917256845631,-927610459464373932427,-36955258706329671973028,535191096878546873823897,23273612576939618406997055,-362206459402896340382856127

%N G.f. A(x) satisfies: Sum_{n>=0} Product_{k=1..n} (n+1-k)*x + k*A(x)  =  1.

%H Paul D. Hanna, <a href="/A306087/b306087.txt">Table of n, a(n) for n = 1..150</a>

%F G.f. A(x) satisfies: A(A(x)) = x.

%e G.f.: A(x) = -x + x^2 - x^3 - 2*x^4 + 8*x^5 + 56*x^6 - 281*x^7 - 3061*x^8 + 18612*x^9 + 271129*x^10 - 1925781*x^11 - 34967550*x^12 + 284063311*x^13 + 6174304311*x^14 - 56535769915*x^15 - 1431894779510*x^16 + ...

%e such that

%e 1  =  1  +  (x + A(x))  +  (x + 2*A(x))*(2*x + A(x))  +  (x + 3*A(x))*(2*x + 2*A(x))*(3*x + A(x))  +  (x + 4*A(x))*(2*x + 3*A(x))*(3*x + 2*A(x))*(4*x + A(x))  +  (x + 5*A(x))*(2*x + 4*A(x))*(3*x + 3*A(x))*(4*x + 2*A(x))*(5*x + A(x)) + ...

%e also, A(A(x)) = x.

%o (PARI) {a(n) = my(A=[-1]); for(i=1,n, A = concat(A,0); A[#A] = -Vec( sum(n=0,#A, prod(k=1,n, (n+1-k)*x + (k)*x*Ser(A) ) ) )[#A+1] );A[n]}

%o for(n=1,30, print1(a(n),", "))

%Y Cf. A306090.

%K sign

%O 1,4

%A _Paul D. Hanna_, Jun 23 2018