cp's OEIS Frontend

A327021 a(n) = (2*n-1)! / 2^(n-1) if n > 0 and a(0) = 1.

%I A327021 #6 Aug 21 2019 03:36:17
%S A327021 1,1,3,30,630,22680,1247400,97297200,10216206000,1389404016000,
%T A327021 237588086736000,49893498214560000,12623055048283680000,
%U A327021 3786916514485104000000,1329207696584271504000000,539658324813214230624000000,250941121038144617240160000000,132496911908140357902804480000000
%N A327021 a(n) = (2*n-1)! / 2^(n-1) if n > 0 and a(0) = 1.
%C A327021 A shifted version of A007019.
%F A327021 a(n) = ((2*(n-2)^3 + (n-2)^2)*a(n-2) + (2*(n-2)^3 + 9*(n-2)^2 + 12*n-18)*a(n-1))/n for n >= 2.
%p A327021 A327021 := n -> `if`(n = 0, 1, (2*n-1)! / 2^(n-1)): seq(A327021(n), n = 0..17);
%p A327021 # Alternative:
%p A327021 a := proc(n) option remember; if n < 2 then return 1 fi;
%p A327021 ((2*(n-2)^3 + (n-2)^2)*a(n-2) + (2*(n-2)^3 + 9*(n-2)^2 + 12*n-18)*a(n-1))/n end:
%Y A327021 Cf. A007019.
%K A327021 nonn
%O A327021 0,3
%A A327021 _Peter Luschny_, Aug 20 2019