A350721
a(n) = Sum_{k=0..n} k! * k^(k+n) * Stirling1(n,k).
Original entry on oeis.org
1, 1, 31, 4184, 1495534, 1110325474, 1481505320078, 3225820132807320, 10696978730747904696, 51287741246274865567776, 341442095880058160040860592, 3055472627228313328903357352784, 35788671820468495762774011478900032
Offset: 0
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a[0] = 1; a[n_] := Sum[k! * k^(k+n) * StirlingS1[n, k], {k, 1, n}]; Array[a, 13, 0] (* Amiram Eldar, Feb 03 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=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*log(1+k*x))^k)))
A351133
a(n) = Sum_{k=0..n} k! * k^(2*n) * Stirling1(n,k).
Original entry on oeis.org
1, 1, 31, 3992, 1342294, 932514674, 1161340476698, 2356863300156504, 7278091701243797640, 32477694155566998880608, 201155980661221409458717152, 1674230688936725338278370413264, 18235249164492209082483584810706528
Offset: 0
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a[0] = 1; a[n_] := Sum[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, k!*k^(2*n)*stirling(n, k, 1));
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first(n)=my(x='x+O('x^(n+1))); 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)))
A351138
a(n) = Sum_{k=0..n} (-1)^(n-k) * k! * k^(k*n) * Stirling1(n,k).
Original entry on oeis.org
1, 1, 33, 118484, 103098352618, 35763050751038414134, 7426387531294394110580641088438, 1294894837982331434068068403253026516109577144, 253092742000650212462862632240661689524832716838851180353875064
Offset: 0
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a[0] = 1; a[n_] := Sum[(-1)^(n - k) * 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, (-1)^(n-k)*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)))
Showing 1-4 of 4 results.