A249931 - OEIS

%I #3 Nov 27 2014 17:07:23

%S 1,1,8,152,3550,92788,2597399,76156625,2308825896,71786597460,

%T 2276556265566,73352261863414,2394513305129959,79024386863955715,

%U 2632253500369515600,88379408361414983552,2987975394537672941171,101633132452812322479087,3475524159518622818586778

%N  G.f. A(x) satisfies: 1+x = A(x)^3 + A(x)^5 - A(x)^7.

%F  G.f.: 1 + Series_Reversion(x - 8*x^2 - 24*x^3 - 30*x^4 - 20*x^5 - 7*x^6 - x^7).

%e  G.f.: A(x) = 1 + x + 8*x^2 + 152*x^3 + 3550*x^4 + 92788*x^5 +...

%e Related expansions.

%e A(x)^3 = 1 + 3*x + 27*x^2 + 505*x^3 + 11778*x^4 + 307608*x^5 +...

%e A(x)^5 = 1 + 5*x + 50*x^2 + 930*x^3 + 21675*x^4 + 565901*x^5 +...

%e A(x)^7 = 1 + 7*x + 77*x^2 + 1435*x^3 + 33453*x^4 + 873509*x^5 +...

%e where 1+x = A(x)^3 + A(x)^5 - A(x)^7.

%o  (PARI) /* From 1+x = A(x)^3 + A(x)^5 - A(x)^7: */

%o {a(n)=local(A=[1, 1]); for(i=1, n, A=concat(A, 0); A[#A]=-Vec(Ser(A)^3+Ser(A)^5-Ser(A)^7)[#A]); A[n+1]}

%o for(n=0, 25, print1(a(n) , ", "))

%o (PARI) /* From Series Reversion: */

%o {a(n)=local(A=1+serreverse(x - 8*x^2 - 24*x^3 - 30*x^4 - 20*x^5 - 7*x^6 - x^7 + x^2*O(x^n)));polcoeff(A,n)}

%o for(n=0, 25, print1(a(n) , ", "))

%Y  Cf. A249926, A249927, A249928, A249929, A249930, A249932.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Nov 27 2014