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

1, 1, 3, 24, 229, 2449, 28035, 336100, 4165920, 52953884, 686517601, 9042628374, 120669757468, 1627932844657, 22166277534398, 304230231637560, 4204474770868230, 58458984141770754, 817176088436608178, 11477568712206346244, 161897000202383717334, 2292445680627209103645

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

G.f.: 1 + Series_Reversion(x - 3*x^2 - 6*x^3 - 4*x^4 - x^5).

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)).

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).

Example

G.f.: A(x) = 1 + x + 3*x^2 + 24*x^3 + 229*x^4 + 2449*x^5 + 28035*x^6 +...
The g.f. satisfies:
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 +
(A(x)-1)*(A(x)^4-1)*(A(x)^7-1)*(A(x)^10-1)*(A(x)^13-1)/A(x)^65 +...
Related expansions.
A(x)^2 = 1 + 2*x + 7*x^2 + 54*x^3 + 515*x^4 + 5500*x^5 +...
A(x)^4 = 1 + 4*x + 18*x^2 + 136*x^3 + 1295*x^4 + 13816*x^5 +...
A(x)^5 = 1 + 5*x + 25*x^2 + 190*x^3 + 1810*x^4 + 19316*x^5 +...
where 1+x = A(x)^2 + A(x)^4 - A(x)^5.

Prog

(PARI) /* From 1+x = A(x)^2 + A(x)^4 - A(x)^5: */
{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]}
for(n=0, 25, print1(a(n) , ", "))
(PARI) /* From Series Reversion: */
{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)}
for(n=0, 25, print1(a(n) , ", "))

Crossrefs

Cf. A214692, A249927, A249928, A249929, A249930, A249931, A249932.

Sequence in context: A324446 A307514 A225107 * A279651 A001099 A277462

Adjacent sequences: A249923 A249924 A249925 * A249927 A249928 A249929

Keyword

nonn

Author

Paul D. Hanna, Nov 27 2014

Status

approved