A375946
Expansion of e.g.f. 1 / (1 + 3 * log(1 - x))^(4/3).
Original entry on oeis.org
1, 4, 32, 372, 5652, 105936, 2360712, 60956472, 1789413864, 58850914752, 2143354213728, 85629122177760, 3723269780412000, 175035687610956480, 8846458578801144000, 478330017277120767360, 27551501517174431852160, 1684176901225092936990720
Offset: 0
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nmax=17; CoefficientList[Series[1 / (1 + 3 * Log[1-x])^(4/3),{x,0,nmax}],x]*Range[0,nmax]! (* Stefano Spezia, Sep 03 2024 *)
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a007559(n) = prod(k=0, n-1, 3*k+1);
a(n) = sum(k=0, n, a007559(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;
A375689
Expansion of e.g.f. 1 / (1 + 3 * x * log(1 - x))^(2/3).
Original entry on oeis.org
1, 0, 4, 6, 136, 660, 13188, 123480, 2584160, 37044000, 855658800, 16536548160, 428924382720, 10358056051200, 302474317729920, 8701780305254400, 284949736641177600, 9464366170599782400, 345224605512559518720, 12956112412535827353600
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+3*x*log(1-x))^(2/3)))
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a(n) = n!*sum(k=0, n\2, prod(j=0, k-1, 3*j+2)*abs(stirling(n-k, k, 1))/(n-k)!);
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)));
A365599
Expansion of e.g.f. 1 / (1 - 3 * log(1 + x))^(2/3).
Original entry on oeis.org
1, 2, 8, 54, 498, 5868, 83940, 1413480, 27375240, 599437440, 14641665120, 394657325280, 11635613604000, 372469741813440, 12864889063033920, 476870475257550720, 18882021780125953920, 795381867831610978560, 35515223076159203880960
Offset: 0
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a[n_] := Sum[Product[3*j + 2, {j, 0, k - 1}] * StirlingS1[n, k], {k, 0, n}]; Array[a, 19, 0] (* Amiram Eldar, Sep 13 2023 *)
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a(n) = sum(k=0, n, prod(j=0, k-1, 3*j+2)*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 1-6 of 6 results.