A308490
a(0) = 1, a(n) = Sum_{k=1..n} stirling2(n,k) * k^(2*k).
Original entry on oeis.org
1, 1, 17, 778, 70023, 10439451, 2327592658, 725325847443, 301054612941037, 160546901676583432, 106969402879501806589, 87079496403914056543799, 85043317211453886535179728, 98135961356804028347727824541, 132097548629285541942722646521053
Offset: 0
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Join[{1}, Table[Sum[k^(2*k)*StirlingS2[n, k], {k, 1, n}], {n, 1, 20}]]
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k^2*(exp(x)-1))^k/k!))) \\ Seiichi Manyama, Feb 04 2022
A351180
a(n) = Sum_{k=0..n} k^(k+n) * Stirling1(n,k).
Original entry on oeis.org
1, 1, 15, 635, 53112, 7367444, 1529130770, 443685287576, 171495189203456, 85174828026304824, 52856314387144232184, 40077340463437963801752, 36457068309928364981668848, 39186634107857517367884040632
Offset: 0
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a[0] = 1; a[n_] := Sum[k^(k + n) * StirlingS1[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, 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/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!)))
A351274
a(0) = 1; thereafter a(n) = Sum_{k=1..n} (2*k)^k * Stirling1(n,k).
Original entry on oeis.org
1, 2, 14, 172, 2964, 65848, 1789688, 57521280, 2133964352, 89744964288, 4219022123328, 219246630903936, 12479659844383104, 772174659456713472, 51603153976362554112, 3704166182571098222592, 284239227254465994240000, 23218955083323248158556160
Offset: 0
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Join[{1},Table[Sum[(2k)^k StirlingS1[n,k],{k,n}],{n,20}]] (* Harvey P. Dale, Dec 31 2023 *)
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a(n) = sum(k=0, n, (2*k)^k*stirling(n, k, 1));
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+lambertw(-2*log(1+x)))))
Showing 1-4 of 4 results.