A074209 -id:A074209 - cp's OEIS frontend

A074309 Sum of next n terms of the form i^i.

4, 283, 50037, 17650540, 10405067904, 9211817140115, 11424093748466841, 18896062057822100616, 40192544399240309019728, 106876212200059543898143707, 347377340594805599176614321101

Offset: 1

Zak Seidov, Sep 22 2002

nonn

Sum of next n terms of the form i^n is A074209. Sum of first n terms of the form i^n is A031971. Sum of first n terms of the form i^i is A001923.

			a(2) = 283 = 3^3 + 4^4, a(3) = 50037 = 4^4 + 5^5 + 6^6, a(4) = 17650540 = 5^5 + 6^6 + 7^7 + 8^8, a(5) = 10405067904 = 6^6 + 7^7 + 8^8 + 9^9 + 10^10.

Seiichi Manyama, Table of n, a(n) for n = 1..193

Cf. A001923, A031971, A074209.

Mathematica
```
Table[Sum[i^i, {i, n+1, 2n}], {n, 20}]
```

a(n) = sum(k=n+1, 2*n, k^k); \\ Seiichi Manyama, Dec 05 2021

a(n) = Sum_{i=n+1..2n} i^i.

a(n) ~ (2*n)^(2*n). - Vaclav Kotesovec, Dec 06 2021

A349928 a(n) = Sum_{k=0..n} (k+n)^k.

Original entry on oeis.org

1, 3, 20, 246, 4481, 107129, 3157836, 110504876, 4473749677, 205615442135, 10574135574388, 601527803412298, 37500537926181449, 2542321872054610333, 186209553386691383388, 14653121207168215024624, 1232879877057607865696085, 110444572988776439826640683

Offset: 0

Seiichi Manyama, Dec 05 2021

nonn

Cf. A026898, A031973, A050409, A060946, A062970, A074209, A116149, A117887.

a[0] = 1; a[n_] := Sum[(k + n)^k, {k, 0, n}]; Array[a, 18, 0] (* Amiram Eldar, Dec 05 2021 *)

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

a(n) ~ 2^n * n^n. - Vaclav Kotesovec, Dec 06 2021

cp's OEIS Frontend

A074309 Sum of next n terms of the form i^i.

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