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A060350
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The sum over all subsets S of [n] of the squares of the number of permutations with descent set =S.
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2
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1, 2, 10, 88, 1216, 24176, 654424, 23136128, 1035227008, 57186502912, 3822411268864, 304059285928960, 28385946491599360, 3073391215118186496, 381995951933025287680, 54020316243835807039488, 8624091617045072628121600
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| a(n) = A137782(2n) / A000984(n)
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EXAMPLE
| a(1)=1^2; a(2)=1^2+1^2; a(3)=1^2+2^2+2^2+1^2; a(4)=1^2+3^2+5^2+3^2+3^2+5^2+3^2+1^2;
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MAPLE
| ct := proc(k) option remember; local i, out, n; if k=0 then RETURN(1); fi; n := floor(evalf(log[2](k)))+1; if k=2^n or k=2^(n+1)-1 then RETURN(1); fi; out := 0; for i from 1 to n do if irem(iquo(k, 2^(i-1)), 2) = 1 and irem(iquo(2*k, 2^(i-1)), 2) =0 then out := out+(n-1)!/(i-1)!/(n-i)!* ct(floor(irem(k, 2^(i-1))+2^(i-2)))*ct(iquo(k, 2^i)); fi; od; out; end: seq(add(ct(i)^2, i=2^(n-1)..2^n-1), n=1..15);
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CROSSREFS
| Cf. A060351.
Sequence in context: A111811 A186448 A144002 * A096658 A186184 A055779
Adjacent sequences: A060347 A060348 A060349 * A060351 A060352 A060353
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KEYWORD
| nonn
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AUTHOR
| Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Mar 31 2001
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EXTENSIONS
| Two more terms from Max Alekseyev (maxale(AT)gmail.com), May 06 2009
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