A365602
Expansion of e.g.f. 1 / (1 - 5 * log(1 + x))^(3/5).
Original entry on oeis.org
1, 3, 21, 246, 3990, 82800, 2092560, 62343600, 2139137760, 83064002160, 3600715721040, 172353630085920, 9028586395211040, 513740204261763840, 31553316959017737600, 2080500578006553619200, 146577866381052082876800, 10988979300484733769667200
Offset: 0
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a[n_] := Sum[Product[5*j + 3, {j, 0, k - 1}] * StirlingS1[n, k], {k, 0, n}]; Array[a, 18, 0] (* Amiram Eldar, Sep 13 2023 *)
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a(n) = sum(k=0, n, prod(j=0, k-1, 5*j+3)*stirling(n, k, 1));
A365603
Expansion of e.g.f. 1 / (1 - 5 * log(1 + x))^(4/5).
Original entry on oeis.org
1, 4, 32, 404, 6924, 150000, 3927480, 120582360, 4246964280, 168767136000, 7468938047520, 364284571992480, 19412919898230240, 1122216138563359680, 69941868616009932480, 4675040053248335097600, 333605090142406849939200, 25312518953112479346316800
Offset: 0
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a[n_] := Sum[Product[5*j + 4, {j, 0, k - 1}] * StirlingS1[n, k], {k, 0, n}]; Array[a, 18, 0] (* Amiram Eldar, Sep 13 2023 *)
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a(n) = sum(k=0, n, prod(j=0, k-1, 5*j+4)*stirling(n, k, 1));
A365604
Expansion of e.g.f. 1 / (1 - 5 * log(1 + x)).
Original entry on oeis.org
1, 5, 45, 610, 11020, 248870, 6744350, 213233400, 7704814200, 313199930400, 14146162064400, 702826758144000, 38093116667766000, 2236695336601458000, 141433354184701746000, 9582086196220281456000, 692463727252196674560000
Offset: 0
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a[n_] := Sum[5^k * k! * StirlingS1[n, k], {k, 0, n}]; Array[a, 17, 0] (* Amiram Eldar, Sep 13 2023 *)
With[{nn=20},CoefficientList[Series[1/(1-5*Log[1+x]),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Aug 05 2025 *)
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a(n) = sum(k=0, n, 5^k*k!*stirling(n, k, 1));
Showing 1-3 of 3 results.