A191365
Expansion of e.g.f. (1/(1-x))^exp(x).
Original entry on oeis.org
1, 1, 4, 18, 102, 695, 5485, 49077, 490308, 5404569, 65106103, 850535477, 11972432846, 180605413001, 2906109200293, 49678357272247, 898988188301320, 17167497793440977, 344991795682802331, 7277230501449340417, 160765066207998479698
Offset: 0
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CoefficientList[Series[(1/(1-x))^Exp[x], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 21 2013 *)
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a(n):=sum(sum(binomial(n,i)*k^i*(-1)^(n-k-i)*stirling1(n-i,k),i,0,n-k),k,1,n);
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x)^exp(x))) \\ Seiichi Manyama, May 03 2022
A351880
Expansion of e.g.f. 1 / (1 - x)^cos(x).
Original entry on oeis.org
1, 1, 2, 3, 6, 15, 105, 924, 8204, 73461, 700005, 7323976, 84472146, 1064285027, 14492861747, 211738655608, 3302847261448, 54800458320345, 963864555797385, 17914985159719376, 350861004976886190, 7221748369472388727, 155853930324297011719, 3519121773604369318856
Offset: 0
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nmax = 23; CoefficientList[Series[1/(1 - x)^Cos[x], {x, 0, nmax}], x] Range[0, nmax]!
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my(x='x+O('x^30)); Vec(serlaplace(1/(1-x)^cos(x))) \\ Michel Marcus, Feb 23 2022
A346427
E.g.f.: -log(1 - log(1 + x) * exp(x)).
Original entry on oeis.org
0, 1, 2, 7, 29, 183, 1319, 12122, 124802, 1508581, 20150509, 302637564, 4960500764, 89164162579, 1730245993111, 36241995276276, 812108432244304, 19430625834864633, 493622198791114665, 13283773364613034324, 377224137563670860492, 11278211794764786428831
Offset: 0
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nmax = 21; CoefficientList[Series[-Log[1 - Log[1 + x] Exp[x]], {x, 0, nmax}], x] Range[0, nmax]!
A002741[n_] := A002741[n] = n! Sum[(-1)^k/((n - k) k!), {k, 0, n - 1}]; a[0] = 0; a[n_] := a[n] = -(-1)^n A002741[n] - (1/n) Sum[(-1)^(n - k) Binomial[n, k] A002741[n - k] k a[k], {k, 1, n - 1}]; Table[a[n], {n, 0, 21}]
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my(x='x+O('x^25)); concat(0, Vec(serlaplace(-log(1 - log(1+x) * exp(x))))) \\ Michel Marcus, Jul 19 2021
A351502
Expansion of e.g.f. 1/(1 + log(1 - x)*exp(-x)).
Original entry on oeis.org
1, 1, 1, 2, 10, 59, 373, 2736, 23504, 229029, 2477219, 29473344, 383104588, 5401356583, 82069677701, 1336740758544, 23234632127072, 429259519490985, 8399672396793063, 173538299521211128, 3774815414843398588, 86230662745426403771, 2063931187442813081881
Offset: 0
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With[{nn=30},CoefficientList[Series[1/(1+Log[1-x]Exp[-x]),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, May 03 2023 *)
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1-x)*exp(-x))))
Showing 1-4 of 4 results.
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