A349857
Expansion of Sum_{k>=0} x^k/(1 + k^3 * x).
Original entry on oeis.org
1, 1, 0, -6, 37, 155, -11616, 251940, 783641, -454238419, 29895012768, -757531311386, -106105977022243, 21452688824818775, -2105573104903303616, 16702280440994303008, 48278492787774402969521, -13301912828187822051695559, 1964564462643243537548661568
Offset: 0
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a[n_] := Sum[If[k == n - k == 0, 1, (-k^3)^(n-k)], {k, 0, n}]; Array[a, 19, 0] (* Amiram Eldar, Dec 03 2021 *)
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a(n, s=0, t=3) = sum(k=0, n, (-k^t)^(n-k)*k^s);
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my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1+k^3*x)))
A349858
Expansion of Sum_{k>=0} x^k/(1 + k^4 * x).
Original entry on oeis.org
1, 1, 0, -14, 175, 2211, -400994, 25610260, 582496701, -666933657755, 166042332973276, -14222991979095594, -14297382182023795925, 12622343477815735821511, -5840589387156997753180230, -443718496524920696265166664, 5189349322544398120691167482361
Offset: 0
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a[n_] := Sum[If[k == n - k == 0, 1, (-k^4)^(n-k)], {k, 0, n}]; Array[a, 17, 0] (* Amiram Eldar, Dec 03 2021 *)
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a(n, s=0, t=4) = sum(k=0, n, (-k^t)^(n-k)*k^s);
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my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1+k^4*x)))
A349884
Expansion of Sum_{k>=0} (k * x)^k/(1 + k^2 * x).
Original entry on oeis.org
1, 1, 3, 12, 76, 961, 15407, 221528, 3260936, 80774113, 2462081967, 50963779604, 922244742292, 61063845514113, 2868669700179871, 2019727494212912, -47889136910252848, 461395118866593115713, 5781219348638565771423, -2108738296748190078596084
Offset: 0
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a[n_] := Sum[If[k == 2*n - k == 0, 1, (-1)^(n - k) * k^(2*n - k)], {k, 0, n}]; Array[a, 20, 0] (* Amiram Eldar, Dec 04 2021 *)
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a(n, t=2) = sum(k=0, n, (-k^t)^(n-k)*k^k);
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my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^k/(1+k^2*x)))
A349894
a(n) = Sum_{k=0..n} (-1)^(n-k) * k^(k*(n-k)).
Original entry on oeis.org
1, 0, 1, -3, -10, 410, 42985, -6527829, -24060996846, -6613442955828, 3882375189467092921, 235121650953066124724477, -289337164954511885810252000250, -995208334663809003504695464745010282, 13325880481925983143500510271865447222057073
Offset: 0
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a(n) = sum(k=0, n, (-1)^(n-k)*k^(k*(n-k)));
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my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1+k^k*x)))
Showing 1-4 of 4 results.