OFFSET
0,5
COMMENTS
Column 0 of A124424.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..400
FORMULA
a(n) = Q[n](0,0,1), where the polynomials Q[n]=Q[n](t,s,x) are defined by Q[0]=1; Q[n]=t*dQ[n-1]/dt + x*dQ[n-1]/ds + x*dQ[n-1]/dx + t*Q[n-1] if n is odd and Q[n]=x*dQ[n-1]/dt + s*dQ[n-1]/ds + x*dQ[n-1]/dx + s*Q[n-1] if n is even.
a(n) = Sum_{k=0..floor(n/2)} Stirling2(floor(n/2),k)*Stirling2(ceiling(n/2),k)*k!. - Alois P. Heinz, Oct 24 2013
EXAMPLE
a(4) = 3 because we have 1234, 14|23 and 12|34.
MAPLE
Q[0]:=1: for n from 1 to 27 do if n mod 2 = 1 then Q[n]:=expand(t*diff(Q[n-1], t)+x*diff(Q[n-1], s)+x*diff(Q[n-1], x)+t*Q[n-1]) else Q[n]:=expand(x*diff(Q[n-1], t)+s*diff(Q[n-1], s)+x*diff(Q[n-1], x)+s*Q[n-1]) fi od: seq(subs({t=0, s=0, x=1}, Q[n]), n=0..27);
# second Maple program:
a:= proc(n) local g, u; g:= floor(n/2); u:= ceil(n/2);
add(Stirling2(g, k)*Stirling2(u, k)*k!, k=0..g)
end:
seq(a(n), n=0..30); # Alois P. Heinz, Oct 24 2013
MATHEMATICA
a[n_] := Module[{g=Floor[n/2], u=Ceiling[n/2]}, Sum[StirlingS2[g, k]*StirlingS2[u, k]*k!, {k, 0, g}]]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 26 2015, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Nov 01 2006
STATUS
approved