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a(n) = |Sum_{k=0..n} (-1)^k*(2k)!!|.
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%I #9 Jul 24 2017 11:56:41

%S 1,1,7,41,343,3497,42583,602537,9719383,176075177,3539816023,

%T 78209790377,1883780763223,49127973630377,1379201149390423,

%U 41470672541233577,329725285558734423,45290937289840177577,1633052915424520654423,62144013487721190961577

%N a(n) = |Sum_{k=0..n} (-1)^k*(2k)!!|.

%C a(20) = 19 * 47 * 73 * 54470291 * 700938921577. Thus a(n) are multiples of 19 for n >= 20.

%t Table[Abs@ Sum[(-1)^k*(2 k)!!, {k, 0, n}], {n, 0, 19}] (* _Michael De Vlieger_, Jul 19 2017 *)

%Y Cf. A006882, A138525.

%K easy,nonn

%O 0,3

%A _XU Pingya_, Jul 19 2017