A281435 E.g.f. S(x) satisfies: S(x) = Integral (1 + S(x)^2)^(7/2) dx.

1, 7, 301, 32347, 6476281, 2080072687, 978357441061, 633671918506627, 540647648053353841, 587611403828850167767, 792504001599034713809821, 1298643416767164198145121707, 2541154725546790383213482500201, 5852376595008692595588309106586047, 15669400182952350735653156519506572181, 48261540873448422135971738449165162450387, 169430327422451431526680101559949211638388961

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)^7, where C(x) is described by A281436.

Prog

(PARI) {a(n) = my(S=x, C=1); for(i=1, n, S = intformal( C^7 +x*O(x^(2*n))); C = 1 + intformal( S*C^6 ) ); (2*n-1)!*polcoeff(S, 2*n-1)}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A082168 A362658 A096348 * A015005 A209806 A257919

Adjacent sequences: A281432 A281433 A281434 * A281436 A281437 A281438

Keyword

nonn

Author

Paul D. Hanna, Jan 21 2017

Status

approved