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A199548 G.f. satisfies: A(x) = Sum_{n>=0} x^n * (1 - A(x)^(2*n+1))/(1 - A(x)). 2
1, 3, 14, 88, 650, 5257, 45017, 401010, 3677344, 34481492, 329082191, 3186043296, 31214870385, 308901931412, 3083146893716, 31001118379636, 313734072027372, 3193097704841990, 32662597147529218, 335616736745247652, 3462524444288857191, 35853293611333010079 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Compare to g.f. B(x) of A007317 (binomial transform of Catalan numbers):

B(x) = Sum_{n>=0} x^n * (1 - B(x)^(n+1))/(1 - B(x)).

LINKS

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

FORMULA

G.f. satisfies: A(x) = 1 + x*A(x)*(2 + A(x)^2) - x^2*A(x)^3.

G.f. satisfies: x = (2 + A(x)^2 - sqrt(4 + 4*A(x) + A(x)^4))/(2*A(x)^2).

EXAMPLE

G.f.: A(x) = 1 + 3*x + 14*x^2 + 88*x^3 + 650*x^4 + 5257*x^5 +...

where g.f. A = A(x) satisfies the equivalent expressions:

A = 1 + x*(1-A^3)/(1-A) + x^2*(1-A^5)/(1-A) + x^3*(1-A^7)/(1-A) +...

A = 1 + x*(1 + A + A^2) + x^2*(1 + A + A^2 + A^3 + A^4) + x^3*(1 + A + A^2 + A^3 + A^4 + A^5 + A^6) +...

PROG

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, x^m*sum(k=0, 2*m, A^k)+x*O(x^n))); polcoeff(A, n)}

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x*A*(2+A^2)-x^2*A^3+x*O(x^n)); polcoeff(A, n)}

CROSSREFS

Cf. A007317.

Sequence in context: A335849 A185323 A222714 * A038170 A007840 A007549

Adjacent sequences:  A199545 A199546 A199547 * A199549 A199550 A199551

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 07 2011

STATUS

approved

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Last modified August 14 09:14 EDT 2020. Contains 336480 sequences. (Running on oeis4.)