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a(1) = 1, a(2) = 2, a(3) = 2, a(4) = 3, for n >= 3, a(n+2) = a(n+1) + a(n)*floor(n/2)*ceiling(n/2).
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%I #15 Aug 04 2020 14:04:34

%S 1,2,2,3,7,19,61,232,964,4676,23956,140856,859536,5930352,42030864,

%T 332618112,2686346496,23973905664,217390853376,2159277212160,

%U 21724454016000,237652175232000,2627342116992000,31383255320064000

%N a(1) = 1, a(2) = 2, a(3) = 2, a(4) = 3, for n >= 3, a(n+2) = a(n+1) + a(n)*floor(n/2)*ceiling(n/2).

%H Harvey P. Dale, <a href="/A098738/b098738.txt">Table of n, a(n) for n = 1..507</a>

%F If a(n) = c(n)*(floor((n-1)/2))!*(ceiling((n-1)/2))!, then for n >= 3, c(n) = the continued fraction [1; 1, 1, 1/2, 1/2, 1/3, 1/3, 1/4, 1/4, ..., ceiling((n-2)/2)], where the total number of rational terms in the continued fraction is (n-1); and c(n+1) also equals, for n>= 3, (Sum_{j=0..floor((n-1)/2)} c(n- 2j)) / ceiling(n/2).

%p a:=array(1..35):a[1]:=1:a[2]:=2:a[3]:=2:a[4]:=3:for n from 3 to 33 do:a[n+2]:=a[n+1]+a[n]*floor(n/2)*ceil(n/2):od:seq(a[i],i=1..35) # Mark Hudson, Oct 21 2004

%t nxt[{n_,a_,b_}]:={n+1,b,b+a*Floor[(n+1)/2]*Ceiling[(n+1)/2]}; Join[ {1,2},Rest[ NestList[nxt,{1,1,2},30][[All,2]]]] (* _Harvey P. Dale_, Aug 04 2020 *)

%K nonn

%O 1,2

%A _Leroy Quet_, Sep 30 2004

%E More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Oct 21 2004