1,3

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]

Thomas Wieder, Home Page.

Thomas Wieder, (Old) Home Page.

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.

a(4)=21 because 1 + 4*1 + 4*4 = 21.

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

Cf. A131407, A131408, A079750.

Sequence in context: A058308 A078591 A090366 this_sequence A104982 A001909 A052852

Adjacent sequences: A131962 A131963 A131964 this_sequence A131966 A131967 A131968

nonn

Thomas Wieder (thomas.wieder(AT)t-online.de), Aug 02 2007

More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 10 2007