A349880
Expansion of Sum_{k>=0} x^k/(1 - k^3 * x).
Original entry on oeis.org
1, 1, 2, 10, 93, 1307, 28002, 842196, 33388393, 1717595949, 111931584098, 8979468552886, 872315432217509, 101425775048588759, 13924209725224120770, 2229705716369149960592, 412760812611799202662609, 87644186710319273062637625, 21180850892383599137766296770
Offset: 0
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a(n, s=0, t=3) = sum(k=0, n, k^(t*(n-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)))
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
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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 *)
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a(n, s=0, t=2) = sum(k=0, n, (-k^t)^(n-k)*k^s);
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my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1+k^2*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)))
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.