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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, 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
Sequence in context: A162478 A348615 A189392 * A065892 A139183 A174705
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 07 2014
STATUS
approved

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Last modified May 25 16:30 EDT 2024. Contains 372801 sequences. (Running on oeis4.)