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)))
A351181
a(n) = Sum_{k=0..n} k^(k+n) * Stirling2(n,k).
Original entry on oeis.org
1, 1, 17, 826, 79107, 12553011, 2979141058, 988163147091, 436562014218313, 247800100563125728, 175732698005376526429, 152264214647249387402567, 158273183995563848011907696, 194391589002961482387840145341
Offset: 0
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a[0] = 1; a[n_] := Sum[k^(k + n) * StirlingS2[n, k], {k, 1, n}]; Array[a, 14, 0] (* Amiram Eldar, Feb 04 2022 *)
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a(n) = sum(k=0, n, k^(k+n)*stirling(n, k, 2));
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*(exp(k*x)-1))^k/k!)))
A351281
a(n) = Sum_{k=0..n} k! * k^k * Stirling2(n,k).
Original entry on oeis.org
1, 1, 9, 187, 7173, 440611, 39631509, 4910795107, 802015652853, 166948755155971, 43146953460348309, 13555255072473665827, 5087595330217093070133, 2248298922174973220446531, 1155512971750307157457879509, 683392198848998191062416885347
Offset: 0
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a[0] = 1; a[n_] := Sum[k! * k^k * StirlingS2[n, k], {k, 1, n}]; Array[a, 16, 0] (* Amiram Eldar, Feb 06 2022 *)
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a(n) = sum(k=0, n, k!*k^k*stirling(n, k, 2));
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*(exp(x)-1))^k)))
A354674
a(n) = Sum_{k=0..n} k! * k^(k+n) * |Stirling1(n,k)|.
Original entry on oeis.org
1, 1, 33, 4568, 1653010, 1236180194, 1657339714418, 3620923498508952, 12037504737979759944, 57827877567223173191712, 385581993722741959459382352, 3454851578510897594456017095504, 40509304222426523176427339597382336
Offset: 0
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a(n) = sum(k=0, n, k!*k^(k+n)*abs(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)))
Showing 1-4 of 4 results.