A375945
Expansion of e.g.f. 1 / (1 + 2 * log(1 - x))^(3/2).
Original entry on oeis.org
1, 3, 18, 156, 1758, 24342, 399480, 7577700, 163090500, 3926104860, 104520733560, 3048811591680, 96695722690200, 3312942954681240, 121938065727180480, 4798400761979259120, 201030443703421854480, 8933622147642363338160, 419725992843354254228640
Offset: 0
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nmax=18; CoefficientList[Series[1 / (1 + 2 * Log[1 - x])^(3/2),{x,0,nmax}],x]*Range[0,nmax]! (* Stefano Spezia, Sep 03 2024 *)
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a001147(n) = prod(k=0, n-1, 2*k+1);
a(n) = sum(k=0, n, a001147(k+1)*abs(stirling(n, k, 1)));
A375951
Expansion of e.g.f. 1 / (1 + 3 * log(1 - x))^(5/3).
Original entry on oeis.org
1, 5, 45, 570, 9270, 183840, 4299360, 115795920, 3528915840, 120032889840, 4507313333040, 185185602462240, 8262852630732000, 397873645339668480, 20563762111640910720, 1135441077379757372160, 66703342626913255770240, 4154100873615633462894720
Offset: 0
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nmax=17; CoefficientList[Series[1 / (1 + 3 * Log[1-x])^(5/3),{x,0,nmax}],x]*Range[0,nmax]! (* Stefano Spezia, Sep 03 2024 *)
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a008544(n) = prod(k=0, n-1, 3*k+2);
a(n) = sum(k=0, n, a008544(k+1)*abs(stirling(n, k, 1)))/2;
A375988
Expansion of e.g.f. (1 + 3 * log(1 - x))^(4/3).
Original entry on oeis.org
1, -4, 0, 12, 108, 1104, 14136, 225768, 4386168, 100885248, 2683789344, 81047258208, 2737919298528, 102266990392896, 4184016413001408, 186047367206499072, 8933002185371731200, 460580247564830138880, 25378595790818821816320, 1488230641037882346324480
Offset: 0
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a(n) = sum(k=0, n, prod(j=0, k-1, 3*j-4)*abs(stirling(n, k, 1)));
A375989
Expansion of e.g.f. (1 + 3 * log(1 - x))^(5/3).
Original entry on oeis.org
1, -5, 5, 30, 180, 1410, 14790, 203880, 3559560, 75659760, 1893764160, 54430097760, 1763357958000, 63501756552720, 2514747808468080, 108572621062573440, 5074353268651935360, 255201626973301102080, 13740802156877800538880, 788580746923723472839680
Offset: 0
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a(n) = sum(k=0, n, prod(j=0, k-1, 3*j-5)*abs(stirling(n, k, 1)));
Showing 1-4 of 4 results.