A365588
Expansion of e.g.f. 1 / (1 + 5 * log(1-x)).
Original entry on oeis.org
1, 5, 55, 910, 20080, 553870, 18333050, 707959800, 31244562600, 1551289408800, 85579293493200, 5193226343508000, 343790892166398000, 24655487205067386000, 1904221630155352038000, 157574022827034258192000, 13908505761692419540320000
Offset: 0
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a[n_] := Sum[5^k * k! * Abs[StirlingS1[n, k]], {k, 0, n}]; Array[a, 17, 0] (* Amiram Eldar, Sep 13 2023 *)
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a(n) = sum(k=0, n, 5^k*k!*abs(stirling(n, k, 1)));
A365587
Expansion of e.g.f. 1 / (1 + 5 * log(1-x))^(4/5).
Original entry on oeis.org
1, 4, 40, 620, 13020, 345120, 11049960, 414711720, 17851113720, 866838536640, 46873882199520, 2793214943693280, 181854240448514400, 12842833148474299200, 977822088984613771200, 79842750450344086867200, 6959878576257689846265600
Offset: 0
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a[n_] := Sum[Product[5*j + 4, {j, 0, k - 1}] * Abs[StirlingS1[n, k]], {k, 0, n}]; Array[a, 17, 0] (* Amiram Eldar, Sep 13 2023 *)
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a(n) = sum(k=0, n, prod(j=0, k-1, 5*j+4)*abs(stirling(n, k, 1)));
A365586
Expansion of e.g.f. 1 / (1 + 5 * log(1-x))^(3/5).
Original entry on oeis.org
1, 3, 27, 390, 7770, 197520, 6108720, 222585360, 9337369920, 443180705520, 23478556469040, 1373311758143520, 87902002849402080, 6111187336982764800, 458573390187299798400, 36939974397639066086400, 3179423992959428231894400, 291190738388834303603395200
Offset: 0
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a[n_] := Sum[Product[5*j + 3, {j, 0, k - 1}] * Abs[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)*abs(stirling(n, k, 1)));
A365601
Expansion of e.g.f. 1 / (1 - 5 * log(1 + x))^(2/5).
Original entry on oeis.org
1, 2, 12, 130, 1990, 39500, 962540, 27807120, 928991280, 35233882320, 1495508048160, 70233555485520, 3615667144284720, 202470393271792800, 12252576455326384800, 796817209624497196800, 55418456683474326892800, 4104671046431448576787200
Offset: 0
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a[n_] := Sum[Product[5*j + 2, {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+2)*stirling(n, k, 1));
Showing 1-4 of 4 results.