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%I #22 Sep 08 2022 08:44:49
%S 3,16,55,156,399,960,2223,5020,11143,24432,53079,114492,245535,524032,
%T 1113823,2358972,4980375,10485360,22019655,46136860,96468463,
%U 201326016,419429775,872414556,1811938599,3758095600,7784627383,16106126460,33285995583,68719475712
%N Second diagonal of A027537.
%H Vincenzo Librandi, <a href="/A027540/b027540.txt">Table of n, a(n) for n = 2..1000</a>
%F Numerators of sequence a[ n, n-1 ] in (a[ i, j ])^2 where a[ i, j ] = A(i, j)/i! if j <= i, 0 if j > i.
%F a(n) = (n+1)*(2^n - n - 1). - _Vladeta Jovovic_, Aug 18 2002
%F G.f.: x^2*(-3+5*x)/((2*x-1)^2*(x-1)^3). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 14 2009; corrected by _R. J. Mathar_, Sep 16 2009
%F a(n) = Sum_{k=0..n} Sum_{i=0..n} (i-k) * C(n-k,i-2). - _Wesley Ivan Hurt_, Sep 19 2017
%t Table[(n + 1) (2^n - n - 1), {n, 2, 35}] (* _Vincenzo Librandi_, Sep 04 2017 *)
%o (Magma) [(n+1)*(2^n-n-1): n in [2..30]]; // _Vincenzo Librandi_, Sep 04 2017
%Y Cf. A027537.
%K nonn,easy
%O 2,1
%A _Olivier Gérard_
%E More terms from _Vladeta Jovovic_, Aug 18 2002
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