A356673
a(n) = n! * Sum_{k=0..n} k^(3*(n-k))/k!.
Original entry on oeis.org
1, 1, 3, 31, 901, 45741, 3960871, 584698843, 130554106761, 40790044059481, 17681098707667531, 10491554658622447191, 8198225417359164798733, 8172446419302496167191941, 10264848632098736708582150511
Offset: 0
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a(n) = n!*sum(k=0, n, k^(3*(n-k))/k!);
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(k!*(1-k^3*x)))))
A356674
a(n) = n! * Sum_{k=0..n} k^(k*(n-k))/k!.
Original entry on oeis.org
1, 2, 5, 25, 349, 19941, 4440391, 4382699203, 17687865017481, 356274213630958297, 33338407933090938442411, 16214021627369697901867402911, 43817834057167927861655409052462093, 595284492835035398061242850538179192931525
Offset: 0
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Table[n!*(1 + Sum[k^(k*(n-k))/k!, {k, 1, n}]), {n, 0, 12}] (* Vaclav Kotesovec, Nov 27 2022 *)
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a(n) = n!*sum(k=0, n, k^(k*(n-k))/k!);
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(k!*(1-k^k*x)))))
A356687
a(n) = n! * Sum_{k=0..n} k^(2*n)/k!.
Original entry on oeis.org
1, 1, 18, 927, 94876, 16251045, 4210190766, 1543550310211, 764096247603480, 493254380867214249, 404269328278061434810, 411862088865696890314311, 512690851568229926690616948, 768775988931240685277619894157
Offset: 0
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a[n_] := n! * Sum[k^(2*n)/k!, {k, 0, n}]; a[0] = 1; Array[a, 14, 0] (* Amiram Eldar, Aug 23 2022 *)
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a(n) = n!*sum(k=0, n, k^(2*n)/k!);
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k^2*x)^k/(k!*(1-k^2*x)))))
Showing 1-3 of 3 results.