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A349886
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a(n) = Sum_{k=0..n} k^(k*n).
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6
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1, 2, 18, 19749, 4295498995, 298024323402930834, 10314425729813391637014599924, 256923578002288684397369021397408936103993, 6277101735598268377660667072561845282166297358613176925573
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OFFSET
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0,2
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 0..26
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FORMULA
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G.f.: Sum_{k>=0} k^(k^2) * x^k/(1 - k^k * x).
a(n) ~ n^(n^2). - Vaclav Kotesovec, Dec 04 2021
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MATHEMATICA
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Table[1 + Sum[k^(k*n), {k, 1, n}], {n, 0, 10}] (* Vaclav Kotesovec, Dec 04 2021 *)
a[n_] := Sum[If[k == 0, 1, k^(k*n)], {k, 0, n}]; Array[a, 9, 0] (* Amiram Eldar, Dec 04 2021 *)
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PROG
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(PARI) a(n) = sum(k=0, n, k^(k*n));
(PARI) my(N=10, x='x+O('x^N)); Vec(sum(k=0, N, k^k^2*x^k/(1-k^k*x)))
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CROSSREFS
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Cf. A031971, A062970, A249459.
Sequence in context: A191554 A066361 A120929 * A007184 A067765 A293242
Adjacent sequences: A349883 A349884 A349885 * A349887 A349888 A349889
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KEYWORD
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nonn
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AUTHOR
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Seiichi Manyama, Dec 03 2021
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STATUS
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approved
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