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A235374 E.g.f. satisfies: A'(x) = A(x)^6 * A(-x)^4 with A(0) = 1. 6
1, 1, 2, 14, 88, 1096, 11792, 209744, 3211648, 74050816, 1474533632, 41710490624, 1023774788608, 34285617473536, 1001167232079872, 38715438665007104, 1311494550010298368, 57488503079879213056, 2217017970860729434112, 108599775372146808848384 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..390

Vaclav Kotesovec, Recurrence (of order 8)

FORMULA

E.g.f.: 1/(1 - Series_Reversion( Integral (1-x^2)^4 dx )).

a(n) ~ n! * 2^(4/5) * (315/128)^(n+1/5) / (Gamma(1/5) * 5^(1/5) * n^(4/5)). - Vaclav Kotesovec, Jan 29 2014

EXAMPLE

E.g.f.: A(x) = 1 + x + 2*x^2/2! + 14*x^3/3! + 88*x^4/4! + 1096*x^5/5! +...

Related series.

A(x)^6 = 1 + 6*x + 42*x^2/2! + 384*x^3/3! + 4368*x^4/4! + 60096*x^5/5! +...

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

1 - 1/A(x) = x + 8*x^3/3! + 496*x^5/5! + 81728*x^7/7! +...

where Series_Reversion(1 - 1/A(x)) = Integral (1-x^2)^4 dx.

MATHEMATICA

CoefficientList[1/(1 - InverseSeries[Series[Integrate[(1-x^2)^4, x], {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^6*subst(A, x, -x)^4 +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))^4))); n!*polcoeff(A, n)}

for(n=0, 25, print1(a(n), ", "))

CROSSREFS

Cf. A235370, A235371, A235372, A235373.

Sequence in context: A065355 A162478 A189392 * A065892 A139183 A174705

Adjacent sequences:  A235371 A235372 A235373 * A235375 A235376 A235377

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 07 2014

STATUS

approved

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Last modified July 11 01:19 EDT 2020. Contains 335600 sequences. (Running on oeis4.)