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A349964
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a(n) = Sum_{k=0..n} (k*n)^n.
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2
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1, 1, 20, 972, 90624, 13828125, 3133930176, 988501957072, 414139067400192, 222497518123837665, 149143419250000000000, 122020951254446884154196, 119671520043865789861724160, 138593796657903100873209121453
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listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..13.
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FORMULA
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a(n) = n^n * [x^n] Sum_{k>=0} (k * x)^k/(1 - k * x) = n^n * A031971(n).
a(n) ~ c * n^(2*n), where c = 1/(1 - 1/exp(1)) = A185393. - Vaclav Kotesovec, Dec 07 2021
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MATHEMATICA
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a[n_] := Sum[If[k == n == 0, 1, (k*n)^n], {k, 0, n}]; Array[a, 14, 0] (* Amiram Eldar, Dec 07 2021 *)
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PROG
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(PARI) a(n) = sum(k=0, n, (k*n)^n);
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CROSSREFS
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Cf. A031971, A155956, A185393, A349966, A349969,
Sequence in context: A274764 A069578 A269644 * A347856 A128482 A128476
Adjacent sequences: A349961 A349962 A349963 * A349965 A349966 A349967
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KEYWORD
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nonn
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AUTHOR
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Seiichi Manyama, Dec 07 2021
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STATUS
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approved
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