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A338188
E.g.f. A(x) satisfies: A(x) = 1 + Integral (x/A(x)^8)' / (x/A(x)^9)' dx.
7
1, 1, 2, 24, 744, 34176, 2075616, 157568832, 14393032704, 1538998994304, 188690729769216, 26105613952260096, 4024003404180667392, 683958535664738770944, 127094910400081584820224, 25634548712499430131818496, 5577725070392980419364847616, 1302342166610120902145498284032
OFFSET
0,3
LINKS
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
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 15 2020
STATUS
approved