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A216712 G.f.: A(x) = 1 + x*A(x)^3 / ( A(-x)*A(I*x)*A(-I*x) ), where I^2 = -1. 3
1, 1, 4, 22, 140, 514, 3444, 23790, 165932, 774610, 5767268, 42526198, 310791884, 1574532626, 12230311188, 92980917006, 696528653740, 3677761305954, 29231321098692, 226211978983190, 1720430261953036, 9313977313216354, 75106192841523892, 588010633850768622 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..23.

EXAMPLE

G.f.: A(x) = 1 + x + 4*x^2 + 22*x^3 + 140*x^4 + 514*x^5 + 3444*x^6 +...

Related expansions:

A(x)^2 = 1 + 2*x + 9*x^2 + 52*x^3 + 340*x^4 + 1484*x^5 + 9520*x^6 +...

A(x)^3 = 1 + 3*x + 15*x^2 + 91*x^3 + 612*x^4 + 3024*x^5 + 19240*x^6 +...

A(x)^4 = 1 + 4*x + 22*x^2 + 140*x^3 + 969*x^4 + 5264*x^5 + 33800*x^6 +...

A(x)*A(-x) = 1 + 7*x^2 + 252*x^4 + 6496*x^6 + 308820*x^8 + 10966136*x^10 + 582452652*x^12 + 23322250960*x^14 + 1309365750212*x^16 +...

Note that A(x) = 1 + x*A(x)^4/(A(x)*A(-x)*A(I*x)*A(-I*x)) where

A(x)*A(-x)*A(I*x)*A(-I*x) = 1 + 455*x^4 + 590200*x^8 + 1124826664*x^12 + 2538673877080*x^16 + 6294363022919816*x^20 + 16568529053651321656*x^24 +...

Note also that a bisection of 1/A(x)^3 equals a bisection of 1/A(x)^4:

1/A(x)^3 = 1 - 3*x - 6*x^2 - 28*x^3 - 165*x^4 + 273*x^5 - 2292*x^6 +...

1/A(x)^4 = 1 - 4*x - 6*x^2 - 28*x^3 - 165*x^4 + 728*x^5 - 2292*x^6 +...

PROG

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

(PARI) {a(n)=local(A=1+x*O(x^n)); for(i=1, n+1, A=1+x*A^4*exp(-4*sum(m=1, n\4, x^(4*m)*polcoeff(log(A), 4*m))+x*O(x^n))); polcoeff(A, n)}

for(n=0, 30, print1(a(n), ", "))

CROSSREFS

Cf. A143339, A216681, A212527, A216713.

Sequence in context: A200731 A193116 A187254 * A240586 A002293 A181784

Adjacent sequences:  A216709 A216710 A216711 * A216713 A216714 A216715

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 14 2012

STATUS

approved

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Last modified December 13 23:26 EST 2018. Contains 318087 sequences. (Running on oeis4.)