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A131965
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a(n) = 1 + sum_{i=2}^{n-1} n * a(i).
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0
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1, 1, 4, 21, 131, 943, 7701, 70409, 712891, 7921011, 95844233, 1254688141, 17670191319, 266412115271, 4281623281141, 73073037331473, 1319881736799731, 25155393101359579
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| a(n) = 1 + sum_{i=2}^{n-1} 1 * a(i) = 2^n; a(n) = 1 + sum_{i=2}^{n-1} 2 * a(i) = 3^n; etc. It seems that a(n+1)/(n*a(n)) -> 1 for n -> oo. [Comment corrected by Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 10 2007]
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FORMULA
| a(n) = 1 + sum_{i=2}^{n-1} n * a(i); exponential generating function = 4/(x-1)^3*(1+x)+1/(x-1)^3*exp(x)*(x-3)+1/2*(-4-3*x^2+x^3)/(x-1)^3; asymptotic expansion: a(n)/n! = (5/2 + e) n^2 + O(n). Also: (n+1)*a(n-1)+a(n-2)+...+a(2) e.g.=a(5)=6*21+4+1=131.
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EXAMPLE
| a(4)=21 because 1 + 4*1 + 4*4 = 21.
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MAPLE
| rctlnn := proc(n::nonnegint) local j; option remember; if n = 0 then 0; else 1+add(n*procname(j), j=2..n-1); end if; end proc:
a[1] := 1; for n from 2 to 18 do a[n] := 1+sum(n*a[i], i = 2 .. n-1) end do: seq(a[n], n = 1 .. 18); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 10 2007
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CROSSREFS
| Cf. A131407, A131408, A079750.
Sequence in context: A058308 A078591 A090366 * A104982 A195440 A001909
Adjacent sequences: A131962 A131963 A131964 * A131966 A131967 A131968
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KEYWORD
| nonn
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AUTHOR
| Thomas Wieder (thomas.wieder(AT)t-online.de), Aug 02 2007
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 10 2007
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