A338194 E.g.f. A(x) satisfies: A(x) = 1 + Integral (x/A(x))' / (x/A(x)^3)' dx.

1, 1, 4, 42, 828, 24840, 1009440, 51906960, 3232993680, 236644571520, 19911894206400, 1893868822137600, 200939416407576000, 23530201619699174400, 3014512836056949427200, 419416309548107359488000, 62979130153042151656608000, 10151678353264190993682432000

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..200

Formula

a(n) ~ c * d^n * n! / n^(5/2), where d = sqrt(2/3) * (16911 + 6904*sqrt(6))^(1/4) = 11.072739470812936554345083170072269377492655044795793623262140269629... and c = 5^(7/4) / (3*(3*(1551639 + 633454*sqrt(6)))^(1/4) * sqrt(Pi)) = 0.05692012295541497528352214255257209953140265348...

Mathematica

nmax = 20; A = 1; Do[A = 1 + Integrate[D[x/A, x]/D[x/A^3, x], x] + O[x]^nmax, nmax]; CoefficientList[A, x] * Range[0, nmax - 1]!

Prog

(PARI) {a(n) = my(A=1); for(i=1, n, A = 1 + intformal( (x/A)'/(x/A^3 +x*O(x^n))' ); ); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A302701, A303064, A338163, A338187, A338188, A338193.

Sequence in context: A196194 A197323 A197976 * A241030 A143990 A352074

Adjacent sequences: A338191 A338192 A338193 * A338195 A338196 A338197

Keyword

nonn

Author

Vaclav Kotesovec, Oct 15 2020

Status

approved