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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). 0
1, 2, 2, 3, 7, 19, 61, 232, 964, 4676, 23956, 140856, 859536, 5930352, 42030864, 332618112, 2686346496, 23973905664, 217390853376, 2159277212160, 21724454016000, 237652175232000, 2627342116992000, 31383255320064000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..24.

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

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

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Last modified August 20 07:48 EDT 2019. Contains 326143 sequences. (Running on oeis4.)