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A249926 G.f. A(x) satisfies: 1+x = A(x)^2 + A(x)^4 - A(x)^5.

%I A249926 #10 Feb 28 2025 23:12:39
%S A249926 1,1,3,24,229,2449,28035,336100,4165920,52953884,686517601,9042628374,
%T A249926 120669757468,1627932844657,22166277534398,304230231637560,
%U A249926 4204474770868230,58458984141770754,817176088436608178,11477568712206346244,161897000202383717334,2292445680627209103645
%N A249926 G.f. A(x) satisfies: 1+x = A(x)^2 + A(x)^4 - A(x)^5.
%F A249926 G.f.: 1 + Series_Reversion(x - 3*x^2 - 6*x^3 - 4*x^4 - x^5).
%F A249926 G.f. A(x) satisfies: x = Sum_{n>=1} 1/A(x)^(6*n) * Product_{k=1..n} (1 - 1/A(x)^(3*k-2)).
%F A249926 G.f. A(x) satisfies: x = Sum_{n>=1} 1/A(x)^(n*(3*n-1)/2+6*n) * Product_{k=1..n} (A(x)^(3*k-2) - 1).
%e A249926 G.f.: A(x) = 1 + x + 3*x^2 + 24*x^3 + 229*x^4 + 2449*x^5 + 28035*x^6 +...
%e A249926 The g.f. satisfies:
%e A249926 x = (A(x)-1)/A(x)^7 + (A(x)-1)*(A(x)^4-1)/A(x)^17 + (A(x)-1)*(A(x)^4-1)*(A(x)^7-1)/A(x)^30 + (A(x)-1)*(A(x)^4-1)*(A(x)^7-1)*(A(x)^10-1)/A(x)^46 +
%e A249926 (A(x)-1)*(A(x)^4-1)*(A(x)^7-1)*(A(x)^10-1)*(A(x)^13-1)/A(x)^65 +...
%e A249926 Related expansions.
%e A249926 A(x)^2 = 1 + 2*x + 7*x^2 + 54*x^3 + 515*x^4 + 5500*x^5 +...
%e A249926 A(x)^4 = 1 + 4*x + 18*x^2 + 136*x^3 + 1295*x^4 + 13816*x^5 +...
%e A249926 A(x)^5 = 1 + 5*x + 25*x^2 + 190*x^3 + 1810*x^4 + 19316*x^5 +...
%e A249926 where 1+x = A(x)^2 + A(x)^4 - A(x)^5.
%o A249926 (PARI) /* From 1+x = A(x)^2 + A(x)^4 - A(x)^5: */
%o A249926 {a(n)=local(A=[1, 1]); for(i=1, n, A=concat(A, 0); A[#A]=-Vec(Ser(A)^2+Ser(A)^4-Ser(A)^5)[#A]); A[n+1]}
%o A249926 for(n=0, 25, print1(a(n) , ", "))
%o A249926 (PARI) /* From Series Reversion: */
%o A249926 {a(n)=local(A=1+serreverse(x - 3*x^2 - 6*x^3 - 4*x^4 - x^5 + x^2*O(x^n)));polcoeff(A,n)}
%o A249926 for(n=0, 25, print1(a(n) , ", "))
%Y A249926 Cf. A214692, A249927, A249928, A249929, A249930, A249931, A249932.
%K A249926 nonn
%O A249926 0,3
%A A249926 _Paul D. Hanna_, Nov 27 2014