A349856
Expansion of Sum_{k>=0} x^k/(1 + k^2 * x).
Original entry on oeis.org
1, 1, 0, -2, 7, 3, -242, 2032, -3795, -187211, 3860140, -36467310, -284357501, 21796446487, -538332144294, 5605176351652, 182065102478857, -12963817679287959, 422751776737348504, -5483284328996107802, -327213964461103956801, 30082452646697648945899
Offset: 0
-
a[n_] := Sum[If[k == n - k == 0, 1, (-k^2)^(n - k)], {k, 0, n}]; Array[a, 22, 0] (* Amiram Eldar, Dec 03 2021 *)
-
a(n, s=0, t=2) = sum(k=0, n, (-k^t)^(n-k)*k^s);
-
my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1+k^2*x)))
A349891
a(n) = Sum_{k=0..n} (-1)^(n-k) * k^(k*n).
Original entry on oeis.org
1, 0, 16, 19619, 4294436111, 298022124379673232, 10314423867168242405282727694, 256923577039829077600620024397823949901879, 6277101735175093150055816289268196664555481440709896684157
Offset: 0
-
a(n) = sum(k=0, n, (-1)^(n-k)*k^(k*n));
-
my(N=10, x='x+O('x^N)); Vec(sum(k=0, N, k^k^2*x^k/(1+k^k*x)))
A349902
a(n) = Sum_{k=0..n} (-1)^(n-k) * k^(3*n).
Original entry on oeis.org
1, 1, 63, 19172, 16249870, 29458152441, 97813591721181, 537081363012854224, 4535464309375188976956, 55796581668379082029481225, 958824462567528346234944706075, 22255431432328421226838750870120356, 678866987929798923743810982299237129610
Offset: 0
-
Join[{1},Table[Sum[(-1)^(n-k) k^(3n),{k,0,n}],{n,20}]] (* Harvey P. Dale, Apr 12 2022 *)
-
a(n) = sum(k=0, n, (-1)^(n-k)*k^(3*n));
-
my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^3*x)^k/(1+k^3*x)))
Showing 1-3 of 3 results.