A351135
a(n) = Sum_{k=0..n} k! * k^(k*n) * Stirling1(n,k).
Original entry on oeis.org
1, 1, 31, 117716, 103060088854, 35762522985456876854, 7426384178533125493811949517898, 1294894823429942179301223205449027573956692920, 253092741940931724343266089700550691376738432767085871485096840
Offset: 0
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a[0] = 1; a[n_] := Sum[k! * k^(k*n) * StirlingS1[n, k], {k, 1, n}]; Array[a, 9, 0] (* Amiram Eldar, Feb 02 2022 *)
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a(n) = sum(k=0, n, k!*k^(k*n)*stirling(n, k, 1));
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my(N=10, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, log(1+k^k*x)^k)))
A351136
a(n) = Sum_{k=0..n} (-1)^(n-k) * k! * k^(2*n) * Stirling1(n,k).
Original entry on oeis.org
1, 1, 33, 4760, 1814698, 1436035954, 2041681617638, 4736066140912728, 16729538152432476024, 85437808930634601070944, 605822464949212598847700512, 5774077466357788471179323050704, 72030066703292325305595937373723040
Offset: 0
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a[0] = 1; a[n_] := Sum[(-1)^(n - k) * k! * k^(2*n) * StirlingS1[n, k], {k, 1, n}]; Array[a, 13, 0] (* Amiram Eldar, Feb 02 2022 *)
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a(n) = sum(k=0, n, (-1)^(n-k)*k!*k^(2*n)*stirling(n, k, 1));
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (-log(1-k^2*x))^k)))
A351134
a(n) = Sum_{k=0..n} k! * k^(3*n) * Stirling1(n,k).
Original entry on oeis.org
1, 1, 127, 115028, 383611414, 3407421330934, 66396378581670602, 2493320561997330821496, 164454446238949941359354760, 17769323863754938530919641304080, 2978930835291629440372517431365668448, 741834782450714229554166000654848368247568
Offset: 0
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a[0] = 1; a[n_] := Sum[k! * k^(3*n) * StirlingS1[n, k], {k, 1, n}]; Array[a, 12, 0] (* Amiram Eldar, Feb 02 2022 *)
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a(n) = sum(k=0, n, k!*k^(3*n)*stirling(n, k, 1));
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, log(1+k^3*x)^k)))
A351183
a(n) = Sum_{k=0..n} k^(2*n) * Stirling1(n,k).
Original entry on oeis.org
1, 1, 15, 539, 28980, 1295404, -177715720, -88870557952, -11213754156480, 11072302541223336, 8352732988619491824, -1800044600955923261688, -8483589341410812834791040, -2945489916041839476122254560
Offset: 0
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a(n) = sum(k=0, n, k^(2*n)*stirling(n, k, 1));
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, log(1+k^2*x)^k/k!)))
A373858
a(n) = Sum_{k=1..n} k! * k^(2*n-1) * Stirling1(n,k).
Original entry on oeis.org
0, 1, 15, 1268, 317294, 175542694, 181641609214, 315309390376056, 850661260866748728, 3370191684116333977872, 18768704088141613880906736, 141902519646656406912522712848, 1415862822521619228707500717132224, 18210234893009450819658863637633454608
Offset: 0
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nmax=13; Range[0,nmax]!CoefficientList[Series[Sum[(Log[1 + k^2*x])^k / k,{k,nmax}],{x,0,nmax}],x] (* Stefano Spezia, Jun 19 2024 *)
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a(n) = sum(k=1, n, k!*k^(2*n-1)*stirling(n, k, 1));
Showing 1-5 of 5 results.