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Second diagonal of A027537.
5

%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 GĂ©rard_

%E More terms from _Vladeta Jovovic_, Aug 18 2002