A347019 -id:A347019 - cp's OEIS frontend

A346987 Expansion of e.g.f. 1 / (1 + 5 * log(1 - x))^(1/5).

1, 1, 7, 86, 1524, 35370, 1015590, 34757400, 1381147440, 62498177880, 3172764322680, 178566159846480, 11034757650750960, 742773843654742080, 54094804600076176320, 4238009228531321452800, 355400361455423327193600, 31764402860426288679456000, 3014207878695233997923193600

Offset: 0

Ilya Gutkovskiy, Aug 11 2021

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..350

Cf. A007840, A008548, A346978, A346984, A347015, A347016, A347019.

nmax = 18; CoefficientList[Series[1/(1 + 5 Log[1 - x])^(1/5), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Abs[StirlingS1[n, k]] 5^k Pochhammer[1/5, k], {k, 0, n}], {n, 0, 18}]

a[n]:=if n=0 then 1 else sum(n!/(n-k)!*(5/k-4/n)*a[n-k],k,1,n);
makelist(a[n],n,0,50); /* Tani Akinari, Aug 27 2023 */

a(n) = Sum_{k=0..n} |Stirling1(n,k)| * A008548(k).
a(n) ~ n! * exp(n/5) / (Gamma(1/5) * 5^(1/5) * n^(4/5) * (exp(1/5) - 1)^(n + 1/5)). - Vaclav Kotesovec, Aug 14 2021
For n > 0, a(n) = Sum_{k=1..n} (n!/(n-k)!)*(5/k-4/n)*a(n-k). - Tani Akinari, Aug 27 2023

A347023 E.g.f.: 1 / (1 - 6 * log(1 + x))^(1/6).

Original entry on oeis.org

1, 1, 6, 72, 1254, 28794, 819888, 27869316, 1101032100, 49570797780, 2505156062472, 140417898936336, 8644973807845368, 579908437058338920, 42098286646367326368, 3288252917244250703664, 274974019392668843164176, 24510436934573885695407504, 2319947117871178825560902112

Offset: 0

Ilya Gutkovskiy, Aug 11 2021

nonn

In general, for k > 1, if e.g.f. = 1 / (1 - k*log(1 + x))^(1/k), then a(n) ~ n! * exp(1/k^2) / (Gamma(1/k) * k^(1/k) * n^(1 - 1/k) * (exp(1/k) - 1)^(n + 1/k)). - Vaclav Kotesovec, Aug 14 2021

Cf. A006252, A008542, A320343, A346985, A347019, A347020, A347021, A347022.

nmax = 18; CoefficientList[Series[1/(1 - 6 Log[1 + x])^(1/6), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS1[n, k] 6^k Pochhammer[1/6, k], {k, 0, n}], {n, 0, 18}]

a(n) = Sum_{k=0..n} Stirling1(n,k) * A008542(k).

a(n) ~ n! * exp(1/36) / (Gamma(1/6) * 6^(1/6) * n^(5/6) * (exp(1/6) - 1)^(n + 1/6)). - Vaclav Kotesovec, Aug 14 2021

cp's OEIS Frontend

A346987 Expansion of e.g.f. 1 / (1 + 5 * log(1 - x))^(1/5).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Maxima

Formula