A339311 -id:A339311 - cp's OEIS frontend

A343928 a(n) = Sum_{k=0..n} (k!)^n * binomial(n,k).

1, 2, 7, 244, 337061, 24923091206, 139331988275478727, 82607113404338664216300296, 6984967577834038055008791270166057993, 109110690950275218023122492287310115968068596613130, 395940866518366059877297056617763923418318903997411043997258716171

Offset: 0

Seiichi Manyama, May 04 2021

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..30

Cf. A000522, A046662, A072034, A336247, A339311, A343898, A343899, A343929.

a[n_] := Sum[(k!)^n * Binomial[n, k], {k, 0, n} ]; Array[a, 11, 0] (* Amiram Eldar, May 04 2021 *)

a(n) = sum(k=0, n, k!^n*binomial(n, k));

a(n) = [x^n] Sum_{k>=0} (k!)^n * x^k/(1 - x)^(k+1).

a(n) = n! * [x^n] exp(x) * Sum_{k>=0} (k!)^(n-1) * x^k.

A112999 Partial sums of A036740.

Original entry on oeis.org

1, 5, 221, 331997, 24883531997, 139314094387531997, 82606411393217618227531997, 6984964247224120535022357995827531997, 109110688415578301444592123476429107940843827531997

Offset: 1

Jonathan Vos Post, Jan 03 2006

			a(1) = (1!)^1 = 1^1 = 1.
a(2) = (1!)^1 + (2!)^2 = 1^1 + 2^2 = 1 + 4 = 5.
a(3) = (1!)^1 + (2!)^2 + (3!)^3 = 1^1 + 2^2 + 6^3 = 1 + 4 + 216 = 221.

Seiichi Manyama, Table of n, a(n) for n = 1..30
G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 331997

Cf. A000142, A000178, A002109, A036740, A339311.

Table[Sum[Product[m^k,{m,1,k}],{k,1,n}],{n,1,10}] (* Vaclav Kotesovec, Nov 01 2014 *)
Accumulate[Table[(n!)^n,{n,10}]] (* Harvey P. Dale, Dec 23 2019 *)

a(n) = sum(k=1, n, k!^k); \\ Michel Marcus, Nov 30 2020

a(n) = Sum_{k=1..n} (k!)^k.
a(n) = Sum_{k=1..n} (A000142(k))^k.
a(n) = Sum_{k=1..n} A036740(k).
a(n) = Sum_{k=1..n} A002109(k) * A000178(k-1).

cp's OEIS Frontend

A343928 a(n) = Sum_{k=0..n} (k!)^n * binomial(n,k).

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