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%I #8 Apr 05 2016 00:42:16
%S 1,2,10,36,204,1104,7776,57600,505440,4803840,51442560,597784320,
%T 7609593600,104364288000,1541746483200,24329797632000,409042632499200,
%U 7290954768384000,137384159367168000,2727604332085248000,56913717580296192000,1244955414746824704000
%N Second column of triangle A134134 (S2'(2) = S1hat(2)).
%C Sum of the products of the factorials of the partition parts of n+2 into two parts. - _Wesley Ivan Hurt_, Mar 18 2016
%F a(n) = A134134(n+2,2), n>=0.
%F a(n) = Sum_{i=1..floor(n/2)+1} i! * (n-i+2)!. - _Wesley Ivan Hurt_, Mar 18 2016
%e a(2)=10; The partitions of (2)+2 = 4 into two parts are: (3,1) and (2,2). The sum of the products of the factorials of the partition parts is: 3!*1! + 2!*2! = 6 + 4 = 10. - _Wesley Ivan Hurt_, Mar 18 2016
%p A144895:=n->add(i!*(n-i+2)!, i=1..floor(n/2)+1): seq(A144895(n), n=0..30); # _Wesley Ivan Hurt_, Mar 18 2016
%t Table[Sum[i!*(n - i + 2)!, {i, Floor[n/2] + 1}], {n, 0, 20}] (* _Wesley Ivan Hurt_, Mar 18 2016 *)
%Y Cf. A000142 (factorials, first column). A144896 (third column).
%Y Cf. A134134.
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Oct 09 2008
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