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Numerator of (-1)^n*n!*(E(n,2)-E(n,1)*E(n-1,1)) where E(n,x) = Sum_{k=0..n} (-1)^k*x^k/k!.
4

%I #11 Apr 14 2024 08:45:07

%S 1,1,2,3,5,17,89,211,1903,62473,89393,1324937,199986173,1248315547,

%T 25821989299,1754517215113,1308752009069,34794177047129,

%U 32791050165840089,37082480057069939,109598046569166901,7850794626671440751,1049848025022301180127,47709314255406993620857

%N Numerator of (-1)^n*n!*(E(n,2)-E(n,1)*E(n-1,1)) where E(n,x) = Sum_{k=0..n} (-1)^k*x^k/k!.

%e 1, 1, 2, 3, 5, 17/2, 89/6, 211/8, 1903/40, 62473/720, ...

%p E := proc(n,x) add((-1)^k*x^k/k!,k=0..n); end; f := n -> (-1)^n*n!*(E(n,2)-E(n,1)*E(n-1,1));

%t e[n_,x_]:=Sum[(-x)^k/k!,{k,0,n}]; a[n_]:=Numerator[(-1)^n*n!*(e[n,2]-e[n,1]e[n-1,1])]; Array[a,24,0] (* _Stefano Spezia_, Apr 12 2024 *)

%Y Cf. A065953 (denominator), A065954, A065955, A065956.

%K nonn,frac

%O 0,3

%A _N. J. A. Sloane_, Dec 08 2001

%E a(0)=1 prepended by and a(23) from _Stefano Spezia_, Apr 12 2024