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Search: id:A003101
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| A003101 |
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Sum_{k = 1..n} (n-k+1)^k.
(Formerly M2745)
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+0
16
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| 0, 1, 3, 8, 22, 65, 209, 732, 2780, 11377, 49863, 232768, 1151914, 6018785, 33087205, 190780212, 1150653920, 7241710929, 47454745803, 323154696184, 2282779990494, 16700904488705, 126356632390297
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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R. K. Hoeflin, Mega Test
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EXAMPLE
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For n = 3 we get a(3) = 3^1 + 2^2 + 1^3 = 8. For n = 4 we get a(4) = 4^1 + 3^2 + 2^3 + 1^4 = 22.
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MAPLE
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A003101 := n->add((n-k+1)^k, k=1..n);
P:=proc(n) local a, i, k; for i from 0 by 1 to n do k:=i; a:=0; while k>0 do a:=a+k^(i-k+1); k:=k-1; od; print(a); od; end: P(100); - Paolo P. Lava (ppl(AT)spl.at), Feb 29 2008
a:=n->sum((n-j)^j, j=1..n): seq(a(n), n=1..23); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 07 2008
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CROSSREFS
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a(n) = A026898(n)-1
First differences are in A047970.
Cf. A062810.
Sequence in context: A014138 A099324 A117420 this_sequence A064443 A000732 A092090
Adjacent sequences: A003098 A003099 A003100 this_sequence A003102 A003103 A003104
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KEYWORD
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nonn,easy
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AUTHOR
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njas, H. W. Gould
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