A281443 E.g.f. S(x) satisfies: S(x) = Integral (1 + S(x)^2)^(9/2) dx.

1, 9, 513, 73737, 19832769, 8579840841, 5445003346497, 4764370917991113, 5496694973220383361, 8084246464894865788809, 14762694711793154790084993, 32769963553535754858524377737, 86898373859771331049009442719809, 271302297590897772500098532033111241, 985007641595004757219829801609866106817, 4114936376199336730220297730026151662954313, 19598505312024077134206058809303825114147365121

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)^9, where C(x) is described by A281444.

Prog

(PARI) {a(n) = my(S=x, C=1); for(i=1, n, S = intformal( C^9 +x*O(x^(2*n))); C = 1 + intformal( S*C^8 ) ); (2*n-1)!*polcoeff(S, 2*n-1)}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A102909 A367552 A230671 * A367446 A003398 A015508

Adjacent sequences: A281440 A281441 A281442 * A281444 A281445 A281446

Keyword

nonn

Author

Paul D. Hanna, Jan 21 2017

Status

approved