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A076483 n! * Sum_k{1<=k<=n}(k-1)^k/k!. 2
0, 0, 1, 11, 125, 1649, 25519, 458569, 9433353, 219117905, 5677963451, 162457597961, 5087919552253, 173136159558361, 6361282619516343, 250987334850557369, 10584205713321808529, 475079402305823570849 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..17.

FORMULA

a(n)/(e*a(n-1))-n tends towards -1/2; a(n)/n^n tends towards 1/(e-1).

EXAMPLE

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

CROSSREFS

Row sums of A076482. Cf. 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

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Last modified September 27 10:32 EDT 2020. Contains 337380 sequences. (Running on oeis4.)