A281427 E.g.f. S(x) satisfies: S(x) = Integral (1 + S(x)^2)^(5/2) dx.

1, 5, 145, 10325, 1357825, 284963525, 87274812625, 36716097543125, 20309401097610625, 14290053364475013125, 12462411363013047060625, 13192751210140624100103125, 16663953549286540157926890625, 24756557919279291667433199453125, 42733906625427778939437818074140625, 84814104213422372894487597292655703125

Offset

1,2

Links

Table of n, a(n) for n=1..16.

Formula

C(x)^2 - S(x)^2 = 1 and S'(x) = C(x)^5, where C(x) is described by A281428.

Mathematica

a[n_] := Module[{S = x, C = 1, C5, SC4}, For[i = 1, i <= n, i++, C5 = C^5 + x*O[x]^(2n) // Normal; S = Integrate[C5, x]; SC4 = S*C^4 + O[x]^(2n-1) // Normal; C = 1 + Integrate[SC4, x] ]; (2n-1)!*Coefficient[S, x, 2n-1]]; Array[a, 16] (* 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^5 +x*O(x^(2*n))); C = 1 + intformal( S*C^4 ) ); (2*n-1)!*polcoeff(S, 2*n-1)}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A076218 A267989 A307902 * A294360 A346084 A075186

Adjacent sequences: A281424 A281425 A281426 * A281428 A281429 A281430

Keyword

nonn

Author

Paul D. Hanna, Jan 21 2017

Status

approved