A346987
Expansion of e.g.f. 1 / (1 + 5 * log(1 - x))^(1/5).
Original entry on oeis.org
1, 1, 7, 86, 1524, 35370, 1015590, 34757400, 1381147440, 62498177880, 3172764322680, 178566159846480, 11034757650750960, 742773843654742080, 54094804600076176320, 4238009228531321452800, 355400361455423327193600, 31764402860426288679456000, 3014207878695233997923193600
Offset: 0
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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}]
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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 */
A347016
Expansion of e.g.f. 1 / (1 + 4 * log(1 - x))^(1/4).
Original entry on oeis.org
1, 1, 6, 62, 916, 17644, 419360, 11859840, 388965600, 14514046560, 607165485120, 28143329181120, 1431690475207680, 79302863940387840, 4751108622148907520, 306118435580577146880, 21107196651940518551040, 1550773243761690603179520, 120947288498720390755353600
Offset: 0
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g:= proc(n) option remember; `if`(n<2, 1, (4*n-3)*g(n-1)) end:
a:= n-> add(abs(Stirling1(n, k))*g(k), k=0..n):
seq(a(n), n=0..18); # Alois P. Heinz, Aug 10 2021
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nmax = 18; CoefficientList[Series[1/(1 + 4 Log[1 - x])^(1/4), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Abs[StirlingS1[n, k]] 4^k Pochhammer[1/4, k], {k, 0, n}], {n, 0, 18}]
A365575
Expansion of e.g.f. 1 / (1 + 3 * log(1-x))^(2/3).
Original entry on oeis.org
1, 2, 12, 114, 1482, 24468, 490020, 11538840, 312363720, 9556741440, 326076452640, 12275391192480, 505400508041760, 22590511357965120, 1089423938332883520, 56379459359942190720, 3116574045158647605120, 183271869976364873222400
Offset: 0
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a[n_] := Sum[Product[3*j + 2, {j, 0, k - 1}] * Abs[StirlingS1[n, k]], {k, 0, n}]; Array[a, 18, 0] (* Amiram Eldar, Sep 11 2023 *)
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a(n) = sum(k=0, n, prod(j=0, k-1, 3*j+2)*abs(stirling(n, k, 1)));
A347020
Expansion of e.g.f. 1 / (1 - 3 * log(1 + x))^(1/3).
Original entry on oeis.org
1, 1, 3, 18, 150, 1644, 22116, 353856, 6554376, 138001896, 3254445144, 84979363248, 2433814616592, 75858381808416, 2556180134677152, 92597465283789312, 3588434497019272320, 148134619713440384640, 6489652665043455707520, 300712023388466713739520
Offset: 0
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nmax = 19; CoefficientList[Series[1/(1 - 3 Log[1 + x])^(1/3), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS1[n, k] 3^k Pochhammer[1/3, k], {k, 0, n}], {n, 0, 19}]
A347019
E.g.f.: 1 / (1 + 6 * log(1 - x))^(1/6).
Original entry on oeis.org
1, 1, 8, 114, 2358, 64074, 2157828, 86714592, 4049302404, 215458069428, 12867377875632, 852254389954296, 61998666080311800, 4914000741835488744, 421488717980664846960, 38897664480760253351904, 3843081247426270376211216, 404727487161912602921083536
Offset: 0
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nmax = 17; CoefficientList[Series[1/(1 + 6 Log[1 - x])^(1/6), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Abs[StirlingS1[n, k]] 6^k Pochhammer[1/6, k], {k, 0, n}], {n, 0, 17}]
A375688
Expansion of e.g.f. 1 / (1 + 3 * x * log(1 - x))^(1/3).
Original entry on oeis.org
1, 0, 2, 3, 56, 270, 4824, 44520, 866816, 12195792, 267873120, 5073187680, 126754229568, 2999710359360, 85061489235072, 2400155295632640, 76724104598031360, 2502434971473937920, 89428428468644493312, 3300036525511418327040
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+3*x*log(1-x))^(1/3)))
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a(n) = n!*sum(k=0, n\2, prod(j=0, k-1, 3*j+1)*abs(stirling(n-k, k, 1))/(n-k)!);
Showing 1-6 of 6 results.
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