A338187 E.g.f. A(x) satisfies: A(x) = 1 + Integral (x/A(x)^3)' / (x/A(x)^4)' dx.

1, 1, 2, 14, 224, 5536, 184576, 7764352, 394918784, 23579517824, 1617167879936, 125302954690816, 10826107873964032, 1032042586785624064, 107609913261744349184, 12183253948487768907776, 1488445213610069857796096, 195181881537478283036065792, 27344175437591659820860309504

Offset

0,3

Links

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

Formula

a(n) ~ 3^(2*n - 5/4) * n^(n-2) / (2^(5/3) * exp(n - 1/6)).

Mathematica

nmax = 20; A = 1; Do[A = 1 + Integrate[D[x/A^3, x]/D[x/A^4, 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^3)'/(x/A^4 +x*O(x^n))' ); ); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A302701, A303064, A338163, A338188, A338193, A338194.

Sequence in context: A153668 A105749 A251692 * A323693 A118086 A048163

Adjacent sequences: A338184 A338185 A338186 * A338188 A338189 A338190

Keyword

nonn

Author

Vaclav Kotesovec, Oct 15 2020

Status

approved