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A147681
Late-growing permutations: number of permutations of 1..n with every partial sum <= the same partial sum averaged over all permutations.
21
1, 1, 1, 3, 7, 35, 139, 1001, 5701, 53109, 402985, 4605271, 43665667, 589809987, 6735960079, 104899483845, 1402547616085, 24698838710457, 378845419610773, 7444522779300351, 128830635114146047, 2792467448952670671, 53854927962971227495, 1276369340371154144337, 27141331409803338993193, 698008560075731437652425, 16228797258964121571885457, 450111715263775132783135875
OFFSET
0,4
COMMENTS
Same as A145874.
LINKS
David Scambler et al., A147681 Late-growing permutations and follow-up messages on the SeqFan list, Aug 10 2012
MAPLE
a:= proc(n) option remember; local b, m; m:= n*(n+1)/2;
b:= proc(s) option remember; local h, g; h:= nops(s);
g:= (n-h+1)*(1+n)/2 -m +add(i, i=s); `if`(h<2, 1,
add(`if`(s[i]<=g, b(subsop(i=NULL, s)), 0), i=1..h))
end; forget(b);
b([$1..n])
end:
seq(a(n), n=0..15); # Alois P. Heinz, Aug 10 2012
MATHEMATICA
a[n_] := a[n] = Module[{b, m}, m = n*(n+1)/2; b[s_List] := b[s] = Module[{h, g}, h = Length[s]; g = (n-h+1)*(1+n)/2 - m + Total[s]; If[h<2, 1, Sum[If[s[[i]] <= g, b[ReplacePart[s, i -> Sequence[]]], 0], {i, 1, h}]]]; b[Range[n]]]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Mar 13 2015, after Alois P. Heinz *)
CROSSREFS
This is the first of 19 related sequences, the others being A147682, A147684, A147686, A147687, A147692, A147694, A147695, A147697, A147698, A147700, A147705, A147707, A147712, A147713, A147714, A147715, A147717, A147769.
Column k=1 of A215561.
Sequence in context: A336012 A212417 A145874 * A055487 A121130 A006099
KEYWORD
nonn,hard
AUTHOR
R. H. Hardin, May 01 2009
EXTENSIONS
a(22) from Alois P. Heinz, Aug 10 2012
a(23) from Alois P. Heinz, Nov 01 2014
a(24)-a(25) from Vaclav Kotesovec, Jan 31 2015
a(26)-a(27) from Vaclav Kotesovec, Sep 07 2016
STATUS
approved