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A281440
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E.g.f. C(x) satisfies: C(x) = cosh( Integral C(x)^7 dx ).
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1
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1, 1, 29, 2605, 478745, 148838425, 70130095925, 46612385237125, 41546401457128625, 47826888286436568625, 69072143074283849778125, 122288686408468623492188125, 260460302659740930298833415625, 657013212464002677825677944215625, 1937092871632377472727255256840753125, 6600357306119497177404312427298619203125, 25738551995192677896309032835665731654390625
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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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C(x)^2 - S(x)^2 = 1 and C(x) = 1 + Integral C(x)^7*S(x) dx, where S(x) is described by A281439.
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MATHEMATICA
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a[n_] := Module[{S = x, C = 1, C8, SC7}, For[i = 0, i <= n, i++, C8 = C^8 + x*O[x]^(2n) // Normal; S = Integrate[C8, x]; SC7 = S*C^7 + O[x]^(2n) // Normal; C = 1+Integrate[SC7, x]]; (2n)!*Coefficient[C, x, 2n]]; Array[a, 17, 0] (* Jean-François Alcover, Mar 01 2017, translated from Pari *)
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PROG
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(PARI) {a(n) = my(S=x, C=1); for(i=0, n, S = intformal( C^8 +x*O(x^(2*n))); C = 1 + intformal( S*C^7 ) ); (2*n)!*polcoeff(C, 2*n)}
for(n=0, 30, 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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