A281432 E.g.f. C(x) satisfies: C(x) = cosh( Integral C(x)^5 dx ).

1, 1, 21, 1341, 173961, 38032281, 12572222301, 5853055718421, 3649908317290641, 2936992590376253361, 2962874009751302380581, 3662113951884448455886701, 5442785335874229886957949721, 9576772316393556595041389524041, 19688717121629473508791582116311661, 46766278604566476892923500929537926981, 127098490344228968075529350992858163636001

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)^5*S(x) dx, where S(x) is described by A281431.

Mathematica

terms = 20; max = 2terms; se = Series[(1/8)*((x*(5+3x^2))/(1+x^2)^2 + 3* ArcTan[x]), {x, 0, max}]; s[x_] = InverseSeries[se, x] // Normal; coes = CoefficientList[Sqrt[1+s[x]^2]+O[x]^(max+1), x]*Range[0, max]!; Partition[ coes, 2][[All, 1]] (* Jean-François Alcover, Mar 01 2017 *)

Prog

(PARI) {a(n) = my(S=x, C=1); for(i=0, n, S = intformal( C^6 +x*O(x^(2*n))); C = 1 + intformal( S*C^5 ) ); (2*n)!*polcoeff(C, 2*n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A250061 A267949 A268096 * A231782 A221733 A298851

Adjacent sequences: A281429 A281430 A281431 * A281433 A281434 A281435

Keyword

nonn

Author

Paul D. Hanna, Jan 21 2017

Status

approved