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A235359 E.g.f. satisfies: A'(x) = A(x)^5 * A(-x)^3 with A(0) = 1. 2
1, 1, 2, 12, 72, 768, 7776, 118656, 1696896, 33623424, 622245888, 15149680128, 344372041728, 9939463852032, 268073031942144, 8944566120382464, 279256558618312704, 10572693702605438976, 375117006060927516672, 15884838808477768876032, 631358485413914656899072 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..20.

Vaclav Kotesovec, Recurrence (of order 6)

FORMULA

E.g.f.: 1/(1 - Series_Reversion( Integral (1-x^2)^3 dx )).

E.g.f. y = A(x) satisfies: 5 - 35*y + 84*y^2 - 70*y^3 + (16-35*x)*y^7 = 0.

a(n) ~ n! * 2^(1/4) * (35/16)^(n+1/4) / (GAMMA(1/4) * n^(3/4)). - Vaclav Kotesovec, Jan 28 2014

EXAMPLE

E.g.f.: A(x) = 1 + x + 2*x^2 + 12*x^3 + 72*x^4 + 768*x^5/5! + 7776*x^6/6! +...

Related series.

A(x)^3 = 1 + 3*x + 12*x^2/2! + 78*x^3/3! + 648*x^4/4! + 6984*x^5/5! +...

A(x)^5 = 1 + 5*x + 30*x^2/2! + 240*x^3/3! + 2400*x^4/4! + 29160*x^5/5! +...

Note that 1 - 1/A(x) is an odd function:

1 - 1/A(x) = x + 6*x^3/3! + 288*x^5/5! + 37008*x^7/7! + 9154944*x^9/9! +...

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

MATHEMATICA

CoefficientList[1/(1 - InverseSeries[Series[x - x^3 + 3*x^5/5 - x^7/7, {x, 0, 20}], x]), x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 28 2014 *)

PROG

(PARI) {a(n)=local(A=1); for(i=0, n, A=1+intformal(A^5*subst(A, x, -x)^3 +x*O(x^n) )); n!*polcoeff(A, n)}

for(n=0, 20, print1(a(n), ", "))

(PARI) {a(n)=local(A=1); A=1/(1-serreverse(intformal((1-x^2 +x*O(x^n))^3))); n!*polcoeff(A, n)}

for(n=0, 20, print1(a(n), ", "))

CROSSREFS

Cf. A234313.

Sequence in context: A335786 A005443 A002867 * A130426 A002397 A163085

Adjacent sequences:  A235356 A235357 A235358 * A235360 A235361 A235362

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 07 2014

STATUS

approved

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Last modified December 3 12:41 EST 2021. Contains 349463 sequences. (Running on oeis4.)