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A236958
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E.g.f. satisfies: A'(x) = A(x)^7 * A(-x)^5 with A(0) = 1.
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5
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1, 1, 2, 16, 104, 1480, 16640, 337600, 5432960, 142650880, 2996614400, 96392704000, 2502799769600, 95198518604800, 2946929024000000, 129296981192704000, 4651138853703680000, 231108723265957888000, 9477883333763366912000, 525848755293052272640000, 24223777158147502407680000
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OFFSET
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0,3
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LINKS
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FORMULA
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E.g.f.: 1/(1 - Series_Reversion( Integral (1 - x^2)^5 dx )).
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EXAMPLE
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E.g.f.: A(x) = 1 + x + 2*x^2/2! + 16*x^3/3! + 104*x^4/4! + 1480*x^5/5! +...
Related series.
A(x)^7 = 1 + 7*x + 56*x^2/2! + 574*x^3/3! + 7280*x^4/4! + 111160*x^5/5! +...
Note that 1 - 1/A(x) is an odd function:
1 - 1/A(x) = x + 10*x^3/3! + 760*x^5/5! + 152800*x^7/7! + 58816000*x^9/9! +...
where Series_Reversion((1 - 1/A(x))) = Integral (1-x^2)^5 dx.
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PROG
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(PARI) {a(n)=local(A=1); for(i=0, n, A=1+intformal(A^7*subst(A^5, x, -x) +x*O(x^n) )); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))
(PARI) {a(n)=local(A=1); A=1/(1-1*serreverse(intformal((1-1*x^2 +x*O(x^n))^(5/1))))^(1/1); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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