A281440 - OEIS

%I #6 Mar 01 2017 11:22:41

%S 1,1,29,2605,478745,148838425,70130095925,46612385237125,

%T 41546401457128625,47826888286436568625,69072143074283849778125,

%U 122288686408468623492188125,260460302659740930298833415625,657013212464002677825677944215625,1937092871632377472727255256840753125,6600357306119497177404312427298619203125,25738551995192677896309032835665731654390625

%N E.g.f. C(x) satisfies: C(x) = cosh( Integral C(x)^7 dx ).

%F 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.

%t 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 *)

%o (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)}

%o for(n=0, 30, print1(a(n), ", "))

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jan 21 2017