A076483 a(n) = n!*Sum_{k=1..n} (k-1)^k/k!.

0, 0, 1, 11, 125, 1649, 25519, 458569, 9433353, 219117905, 5677963451, 162457597961, 5087919552253, 173136159558361, 6361282619516343, 250987334850557369, 10584205713321808529, 475079402305823570849, 22614513693572549266291, 1137911105533216112417161

Offset

0,4

Comments

Perhaps the largest possible number of ways of choosing (v1, v2, ..., vn), possibly with repetition, from {b1, b2, ..., bn} with b1 < b2 < ... < bn, such that v1 + v2 + ... + vn < b1 + b2 + ... + bn. Clearly the actual number of ways depends on the particular values of {b1, b2, ..., bn}, but {1, n, n^2, ..., n^(n-1)} produces this result for the number of sums strictly less than (n^n-1)/(n-1) = A023037(n).

Links

Seiichi Manyama, Table of n, a(n) for n = 0..386

Formula

Limit_{n->oo} a(n)/(e*a(n-1)) - n = -1/2.

Limit_{n->oo} a(n)/n^n = 1/(e-1).

Example

a(4) = 4!*(0^1/1! + 1^2/2! + 2^3/3! + 3^4/4!) = 0 + 12 + 32 + 81 = 125.

Mathematica

Table[n! Sum[(k-1)^k/k!, {k, n}], {n, 0, 17}] (* Stefano Spezia, Sep 11 2022 *)

Prog

(PARI) a(n) = n!*sum(k=1, n, (k-1)^k/k!); \\ Seiichi Manyama, Jul 15 2023

Crossrefs

Row sums of A076482.

Cf. A023037, A075473.

Sequence in context: A015596 A163310 A240335 * A209901 A285056 A015597

Adjacent sequences: A076480 A076481 A076482 * A076484 A076485 A076486

Keyword

nonn

Author

Henry Bottomley, Oct 14 2002

Status

approved