A368505
a(n) = Sum_{k=0..n} n^(n-k) * k^n.
Original entry on oeis.org
1, 1, 6, 60, 900, 18945, 536046, 19750864, 923023368, 53456736825, 3758407535410, 315059660550756, 31005946105301388, 3535337355213234025, 461813139285801522870, 68448013078470849802560, 11415281142784979557384208, 2126537819755999634260404945
Offset: 0
A349883
Expansion of Sum_{k>=0} (k * x)^k/(1 - k^3 * x).
Original entry on oeis.org
1, 1, 5, 60, 1242, 41241, 2033683, 141318208, 13262986788, 1624337451945, 252725477615989, 48858277079478156, 11523986801592238046, 3265676705193282018577, 1097336766468309067029991, 432291795385094609190468384, 197690320046319097006619353352
Offset: 0
-
a[n_] := Sum[If[k == 3*n - 2*k == 0, 1, k^(3*n - 2*k)], {k, 0, n}]; Array[a, 17, 0] (* Amiram Eldar, Dec 04 2021 *)
-
a(n, t=3) = sum(k=0, n, k^(t*(n-k)+k));
-
my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^k/(1-k^3*x)))
A359659
a(n) = Sum_{k=0..n} k^(k * (n-k+1)).
Original entry on oeis.org
1, 2, 6, 45, 1051, 88602, 27121964, 37004504305, 198705527223757, 5595513387083114570, 686714367475480207331582, 468422339816915120237104999421, 1664212116512828935888786624225704855
Offset: 0
-
a(n) = sum(k=0, n, k^(k*(n-k+1)));
-
my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^k/(1-k^k*x)))
-
my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-(k+1)^(k+1)*x)))
Showing 1-3 of 3 results.