%I A097204
%S A097204 0,0,1,8,49,294,1893,13572,109345,985898,9863077,108503064,1302057249,
%T A097204 16926789294,236975148421,3554627439308,56874039487681,966858672273618,
%U A097204 17403456103022277,330665665961879712,6613313319247031425
%N A097204 Binomial transform of A033312.
%C A097204 a(n) = Sum[n!(k!-1) / k!(n-k)! {k=0...n}]
%F A097204 a(n) = Sum[P(n, k) - C(n, k) {k=0...n}]
%e A097204 a(2) = 1 because P(2,0) = 1, P(2,1) = 2, P(2,2) = 2 while C(2,0) = 1, 
               C(2,1) = 2, C(2,2) = 1 and 1 - 1 + 2 - 2 + 2 - 1 = 1.
%p A097204 A033312 := proc(n) factorial(n)-1; end: A097204 := proc(n) add( binomial(n,
               k)*A033312(k),k=1..n) ; end: seq(A097204(n),n=0..30) ; - R. J. Mathar 
               (mathar(AT)strw.leidenuniv.nl), Aug 05 2007
%Y A097204 Cf. A033312.
%Y A097204 Sequence in context: A089383 A028443 A001108 this_sequence A037539 A037483 
               A024106
%Y A097204 Adjacent sequences: A097201 A097202 A097203 this_sequence A097205 A097206 
               A097207
%K A097204 nonn
%O A097204 0,4
%A A097204 Ross La Haye (rlahaye(AT)new.rr.com), Sep 16 2004
%E A097204 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 05 2007