A098738 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).

1, 2, 2, 3, 7, 19, 61, 232, 964, 4676, 23956, 140856, 859536, 5930352, 42030864, 332618112, 2686346496, 23973905664, 217390853376, 2159277212160, 21724454016000, 237652175232000, 2627342116992000, 31383255320064000

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..507

Formula

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).

Maple

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

Mathematica

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 *)

Crossrefs

Sequence in context: A113842 A032161 A265801 * A291742 A083701 A076996

Adjacent sequences: A098735 A098736 A098737 * A098739 A098740 A098741

Keyword

nonn

Author

Leroy Quet, Sep 30 2004

Extensions

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

Status

approved