A338163 O.g.f. A(x) satisfies: A(x) = 1 + Integral (x/A(x)^5)' / (x/A(x)^9)' dx.

1, 1, 4, 34, 431, 6705, 117586, 2231976, 44831130, 939591338, 20356891124, 452951521244, 10301119777824, 238587853086450, 5612274604714104, 133784939985546616, 3226206848503501203, 78591227562499623465, 1931707400018597321796, 47859370196549721964410

Offset

0,3

Comments

If g.f. A(x) satisfies: A(x) = 1 + Integral (x/A(x)^p)' / (x/A(x)^q)' dx, then only for these pairs [p,q] are the coefficients of the series positive integers: [1,4], [4,7], [4,10], [5,9], [8,15], for 1 <= p <= 20, 1 <= q <= 20, p<>q.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..400

Formula

a(n) ~ 2^(n + 1/3) * 3^((3*n - 1)/2) * 5^(5*n/8 - 47/24) / (sqrt(Pi) * n^(5/2)).

Mathematica

nmax = 25; A = 1; Do[A = 1 + Integrate[D[x/A^5, x]/D[x/A^9, x], x] + O[x]^nmax, nmax]; CoefficientList[A, x]

Prog

(PARI) {a(n) = my(A=1); for(i=1, n, A = 1 + intformal( (x/A^5)'/(x/A^9 +x*O(x^n))' ); ); polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A302701, A303064, A338187, A338188, A338193, A338194.

Sequence in context: A236964 A145349 A309170 * A052630 A071213 A052629

Adjacent sequences: A338160 A338161 A338162 * A338164 A338165 A338166

Keyword

nonn

Author

Vaclav Kotesovec, Oct 15 2020

Status

approved