A349966
a(n) = Sum_{k=0..n} (k * (n-k))^n.
Original entry on oeis.org
1, 0, 1, 16, 418, 17600, 1086979, 92223488, 10292241540, 1462309109760, 257739952352133, 55188518041440256, 14111052911099343782, 4246668467339066589184, 1485904567816768099571207, 598145009954138900489830400
Offset: 0
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a[0] = 1; a[n_] := Sum[(k*(n - k))^n, {k, 0, n}]; Array[a, 16, 0] (* Amiram Eldar, Dec 07 2021 *)
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a(n) = sum(k=0, n, (k*(n-k))^n);
A351795
a(n) = n! * Sum_{k=0..n} (k * (n-k))^k/k!.
Original entry on oeis.org
1, 1, 4, 30, 396, 8360, 256470, 10619952, 564959528, 37370475648, 3001942868490, 287388158562560, 32278318416029532, 4197544986996581376, 625014083479647028622, 105554855135062180485120, 20053957030647088382195280, 4255329207190209023134564352
Offset: 0
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a[n_] := n!*(1 + Sum[(k*(n - k))^k/k!, {k, 1, n}]); Array[a, 18, 0] (* Amiram Eldar, Feb 19 2022 *)
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a(n) = n!*sum(k=0, n, (k*(n-k))^k/k!);
A135749
a(n) = Sum_{k=0..n} binomial(n,k)*(n-k)^k*k^k.
Original entry on oeis.org
1, 1, 3, 19, 217, 3821, 95761, 3214975, 137501505, 7226764921, 455941716481, 33983083953611, 2954163633223969, 296027886705639973, 33823026186790043841, 4363561123325076879991, 630392564294402819207041
Offset: 0
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Table[Sum[Binomial[n,k](n-k)^k k^k,{k,n}],{n,0,20}]+1 (* Harvey P. Dale, Oct 08 2012 *)
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a(n)=sum(k=0,n,binomial(n,k)*(n-k)^k*k^k)
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a(n)=n!*polcoeff(sum(k=0,n,exp((n-k)*k*x +x*O(x^n))*x^k/k!),n)
Showing 1-3 of 3 results.
