A349966 -id:A349966 - cp's OEIS frontend

A349965 a(n) = Sum_{k=0..n} (k * (n-k))^k.

1, 1, 2, 7, 47, 513, 8020, 169227, 4637965, 159568981, 6684686230, 332681461871, 19316990453131, 1292074091000105, 98636639620170792, 8528989125071254867, 829516920337723299465, 90124512307642049807293, 10865612430780251465538154

Offset: 0

Seiichi Manyama, Dec 07 2021

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..286

Cf. A026898, A100262, A349966.

a[n_] := Sum[If[k == 0, 1, (k*(n - k))^k], {k, 0, n}]; Array[a, 19, 0] (* Amiram Eldar, Dec 07 2021 *)

PARI
```
a(n) = sum(k=0, n, (k*(n-k))^k);
```

log(a(n)) ~ n*(2*log(n) - 1 + (1/(2*log(n)) - 1)*log(2*log(n))). - Vaclav Kotesovec, Dec 07 2021

A349964 a(n) = Sum_{k=0..n} (k*n)^n.

Original entry on oeis.org

1, 1, 20, 972, 90624, 13828125, 3133930176, 988501957072, 414139067400192, 222497518123837665, 149143419250000000000, 122020951254446884154196, 119671520043865789861724160, 138593796657903100873209121453

Offset: 0

Seiichi Manyama, Dec 07 2021

nonn

Cf. A031971, A155956, A185393, A349966, A349969,

a[n_] := Sum[If[k == n == 0, 1, (k*n)^n], {k, 0, n}]; Array[a, 14, 0] (* Amiram Eldar, Dec 07 2021 *)

PARI
```
a(n) = sum(k=0, n, (k*n)^n);
```

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

cp's OEIS Frontend

A349965 a(n) = Sum_{k=0..n} (k * (n-k))^k.

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