A354750
Expansion of e.g.f. 1 / (1 - log(1 + 3*x) / 3).
Original entry on oeis.org
1, 1, -1, 6, -48, 534, -7542, 129240, -2603736, 60292512, -1577546928, 46021512096, -1480976147664, 52110720451152, -1990258155061776, 81995762243700864, -3624527727510038784, 171109526616468957312, -8591991935936929932672, 457246520477143117555968
Offset: 0
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nmax = 19; CoefficientList[Series[1/(1 - Log[1 + 3 x]/3), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS1[n, k] k! 3^(n - k), {k, 0, n}], {n, 0, 19}]
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my(x='x + O('x^20)); Vec(serlaplace(1/(1-log(1+3*x)/3))) \\ Michel Marcus, Jun 06 2022
A354751
Expansion of e.g.f. 1 / (1 - log(1 + 4*x) / 4).
Original entry on oeis.org
1, 1, -2, 14, -152, 2264, -42832, 982512, -26484096, 820207488, -28692711168, 1118821622016, -48112717347840, 2261868010650624, -115400220781209600, 6350152838136428544, -374874781697133871104, 23632196147497381625856, -1584445791263626895228928
Offset: 0
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nmax = 18; CoefficientList[Series[1/(1 - Log[1 + 4 x]/4), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS1[n, k] k! 4^(n - k), {k, 0, n}], {n, 0, 18}]
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my(x='x + O('x^20)); Vec(serlaplace(1/(1-log(1+4*x)/4))) \\ Michel Marcus, Jun 06 2022
A354752
a(n) = Sum_{k=0..n} Stirling1(n,k) * k! * n^(n-k).
Original entry on oeis.org
1, 1, 0, 6, -152, 6670, -451152, 43685208, -5741360256, 984176280288, -213379094227200, 57100689621382176, -18489130293293779968, 7125765731670143814672, -3223822934974620319272960, 1692009521117003600170128000, -1019755541584493644326799048704
Offset: 0
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Unprotect[Power]; 0^0 = 1; Table[Sum[StirlingS1[n, k] k! n^(n - k), {k, 0, n}], {n, 0, 16}]
Join[{1}, Table[n! SeriesCoefficient[1/(1 - Log[1 + n x]/n), {x, 0, n}], {n, 1, 16}]]
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a(n) = sum(k=0, n, stirling(n, k, 1) * k! * n^(n-k)); \\ Michel Marcus, Jun 06 2022
Showing 1-3 of 3 results.