A281439 E.g.f. S(x) satisfies: S(x) = Integral (1 + S(x)^2)^4 dx.

1, 8, 400, 50240, 11785600, 4441856000, 2454008012800, 1868290095104000, 1874681294061568000, 2397270685274439680000, 3805279100715082055680000, 7340935950235519959695360000, 16914832674388009655153459200000, 45880424534295682918423042457600000, 144703052106498223918408385167360000000, 525071839282110600136335825513218048000000, 2171977104073271071565755547788005867520000000

Offset

1,2

Links

Table of n, a(n) for n=1..17.

Formula

C(x)^2 - S(x)^2 = 1 and S'(x) = C(x)^8, where C(x) is described by A281440.

Mathematica

a[n_] := Module[{S = x, C = 1, C8, SC7}, For[i = 1, 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-1)!*Coefficient[S, x, 2n-1]]; Array[a, 17] (* Jean-François Alcover, Mar 01 2017, translated from Pari *)

Prog

(PARI) {a(n) = my(S=x, C=1); for(i=1, n, S = intformal( C^8 +x*O(x^(2*n))); C = 1 + intformal( S*C^7 ) ); (2*n-1)!*polcoeff(S, 2*n-1)}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A185254 A347997 A221224 * A220550 A191874 A323575

Adjacent sequences: A281436 A281437 A281438 * A281440 A281441 A281442

Keyword

nonn

Author

Paul D. Hanna, Jan 21 2017

Status

approved