A001315 -id:A001315 - cp's OEIS frontend

A087314 a(n) = (1/n) * Sum_{k = 0..n} n^binomial(n,k).

2, 4, 20, 1154, 3907502, 609516468354242, 108233912076063807870514781000, 205688069665244291374160325606433848956971528595913979304345602, 381367496233593231179533022742555015402552706280473714446093438118953849830784189071820024395733993533363857256493600698

Offset: 1

Amarnath Murthy, Sep 03 2003

nonn

			a(3) = 1/3*{ 3^1 +3^3+3^3+3^1} = 20.

Cf. A001315.

a(n) = sum(k = 0, n, n^binomial(n, k))/n; \\ David Wasserman, May 02 2005

More terms from David Wasserman, May 02 2005

A302546 a(n) = Sum_{k = 1...n} 2^binomial(n, k).

Original entry on oeis.org

0, 2, 6, 18, 98, 2114, 1114242, 68723671298, 1180735735906024030722, 170141183460507917357914971986913657858, 7237005577335553223087828975127304179197147198604070555943173844710572689410

Offset: 0

Gus Wiseman, Jun 20 2018

nonn

Cf. A001315, A003465, A034729, A055621, A302545.

Table[Sum[2^Binomial[n,d],{d,n}],{n,10}]

a(n) = sum(k=1, n, 2^binomial(n, k)); \\ Michel Marcus, Jun 21 2018

a(n) = A001315(n) - 2.

A356719 a(n) = Sum_{k=0..n} k^binomial(n,k).

Original entry on oeis.org

0, 1, 3, 12, 150, 61103, 4560574625, 1180642129099670883352, 1395184353688945915375285901200638422723404, 11754943508230112085264929216560108802852371298464244215700837207032911162905441549473573

Offset: 0

Seiichi Manyama, Aug 24 2022

Cf. A001315, A064405, A087314.

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

cp's OEIS Frontend

A087314 a(n) = (1/n) * Sum_{k = 0..n} n^binomial(n,k).

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A302546 a(n) = Sum_{k = 1...n} 2^binomial(n, k).

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Formula

A356719 a(n) = Sum_{k=0..n} k^binomial(n,k).

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