A351182
a(n) = Sum_{k=0..n} k^(2*k) * Stirling1(n,k).
Original entry on oeis.org
1, 1, 15, 683, 61332, 9135004, 2035708760, 634172615600, 263166948202080, 140322186951905736, 93484350581344936344, 76095870609142447018152, 74311960997497053384537408, 85748280952260853814490688656
Offset: 0
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a(n) = sum(k=0, n, k^(2*k)*stirling(n, k, 1));
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k^2*log(1+x))^k/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!)))
A351769
a(n) = Sum_{k=0..n} (-1)^(n-k) * Stirling1(n, k) * k^(k+n).
Original entry on oeis.org
1, 1, 17, 827, 79368, 12623124, 3002832110, 998401869464, 442148442609152, 251578963946182968, 178846127724854653704, 155339277405600252114072, 161863497852092601156187152, 199286757107586767535516731832, 286210094619439661737214469710088
Offset: 0
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Table[Sum[k^(k+n) * StirlingS1[n, k] * (-1)^(n-k), {k, 0, n}], {n, 0, 20}]
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a(n) = sum(k=0, n, (-1)^(n-k)*stirling(n, k, 1)*k^(k+n)); \\ Michel Marcus, Feb 19 2022
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (-k*log(1-k*x))^k/k!))) \\ Seiichi Manyama, Jun 02 2022
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!)))
Showing 1-4 of 4 results.