%I A003101 M2745
%S A003101 0,1,3,8,22,65,209,732,2780,11377,49863,232768,1151914,
%T A003101 6018785,33087205,190780212,1150653920,7241710929,47454745803,
%U A003101 323154696184,2282779990494,16700904488705,126356632390297
%N A003101 Sum_{k = 1..n} (n-k+1)^k.
%D A003101 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A003101 R. K. Hoeflin, <a href="http://www.eskimo.com/~miyaguch/mega.html">Mega 
               Test</a>
%e A003101 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.
%p A003101 A003101 := n->add((n-k+1)^k, k=1..n);
%p A003101 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
%p A003101 a:=n->sum((n-j)^j,j=1..n): seq(a(n), n=1..23); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jun 07 2008
%Y A003101 a(n) = A026898(n)-1
%Y A003101 First differences are in A047970.
%Y A003101 Cf. A062810.
%Y A003101 Sequence in context: A014138 A099324 A117420 this_sequence A064443 A000732 
               A092090
%Y A003101 Adjacent sequences: A003098 A003099 A003100 this_sequence A003102 A003103 
               A003104
%K A003101 nonn,easy
%O A003101 0,3
%A A003101 N. J. A. Sloane (njas(AT)research.att.com), H. W. Gould