A338188 E.g.f. A(x) satisfies: A(x) = 1 + Integral (x/A(x)^8)' / (x/A(x)^9)' dx.

1, 1, 2, 24, 744, 34176, 2075616, 157568832, 14393032704, 1538998994304, 188690729769216, 26105613952260096, 4024003404180667392, 683958535664738770944, 127094910400081584820224, 25634548712499430131818496, 5577725070392980419364847616, 1302342166610120902145498284032

Offset

0,3

Links

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

Formula

a(n) ~ 2^(4*n - 49/18) * n^(n-2) / (3^(11/8) * exp(n - 1/12)).

Mathematica

nmax = 20; A = 1; Do[A = 1 + Integrate[D[x/A^8, x]/D[x/A^9, 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^8)'/(x/A^9 +x*O(x^n))' ); ); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A302701, A303064, A338163, A338187, A338193, A338194.

Sequence in context: A009724 A177771 A009396 * A274634 A292694 A012128

Adjacent sequences: A338185 A338186 A338187 * A338189 A338190 A338191

Keyword

nonn

Author

Vaclav Kotesovec, Oct 15 2020

Status

approved