A281440 E.g.f. C(x) satisfies: C(x) = cosh( Integral C(x)^7 dx ).

1, 1, 29, 2605, 478745, 148838425, 70130095925, 46612385237125, 41546401457128625, 47826888286436568625, 69072143074283849778125, 122288686408468623492188125, 260460302659740930298833415625, 657013212464002677825677944215625, 1937092871632377472727255256840753125, 6600357306119497177404312427298619203125, 25738551995192677896309032835665731654390625

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

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.

Mathematica

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 *)

Prog

(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), ", "))

Crossrefs

Sequence in context: A370339 A316333 A377218 * A171720 A305138 A091751

Adjacent sequences: A281437 A281438 A281439 * A281441 A281442 A281443

Keyword

nonn

Author

Paul D. Hanna, Jan 21 2017

Status

approved