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%I #4 Apr 09 2014 21:03:50
%S 1,1,2,16,104,1480,16640,337600,5432960,142650880,2996614400,
%T 96392704000,2502799769600,95198518604800,2946929024000000,
%U 129296981192704000,4651138853703680000,231108723265957888000,9477883333763366912000,525848755293052272640000,24223777158147502407680000
%N E.g.f. satisfies: A'(x) = A(x)^7 * A(-x)^5 with A(0) = 1.
%F E.g.f.: 1/(1 - Series_Reversion( Integral (1 - x^2)^5 dx )).
%e E.g.f.: A(x) = 1 + x + 2*x^2/2! + 16*x^3/3! + 104*x^4/4! + 1480*x^5/5! +...
%e Related series.
%e A(x)^7 = 1 + 7*x + 56*x^2/2! + 574*x^3/3! + 7280*x^4/4! + 111160*x^5/5! +...
%e Note that 1 - 1/A(x) is an odd function:
%e 1 - 1/A(x) = x + 10*x^3/3! + 760*x^5/5! + 152800*x^7/7! + 58816000*x^9/9! +...
%e where Series_Reversion((1 - 1/A(x))) = Integral (1-x^2)^5 dx.
%o (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)}
%o for(n=0, 20, print1(a(n), ", "))
%o (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)}
%o for(n=0, 20, print1(a(n), ", "))
%Y Cf. A236953, A236954, A236955, A236956, A236957.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Apr 09 2014
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