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Search: id:A076483
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| A076483 |
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n! * Sum_k{1<=k<=n}(k-1)^k/k!. |
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+0
3
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| 0, 0, 1, 11, 125, 1649, 25519, 458569, 9433353, 219117905, 5677963451, 162457597961, 5087919552253, 173136159558361, 6361282619516343, 250987334850557369, 10584205713321808529, 475079402305823570849
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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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).
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FORMULA
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a(n)/(e*a(n-1))-n tends towards -1/2; a(n)/n^n tends towards 1/(e-1).
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EXAMPLE
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a(4)=4!*(0^1/1!+1^2/2!+2^3/3!+3^4/4!)=0+12+32+81=125.
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CROSSREFS
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Row sums of A076482. Cf. A075473.
Adjacent sequences: A076480 A076481 A076482 this_sequence A076484 A076485 A076486
Sequence in context: A121337 A015594 A015596 this_sequence A015597 A141987 A048394
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Oct 14 2002
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