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A182162
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Triangle read by rows: number of extensional acyclic digraphs on n labeled nodes with k sources.
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4
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1, 2, 12, 192, 24, 8160, 2400, 898560, 384480, 14400, 245145600, 126040320, 9777600, 50400, 159035627520, 90043269120, 9660672000, 179222400, 80640, 237882053283840, 141969202744320, 17961178152960, 547498828800, 2586608640, 802369403419852800
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OFFSET
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1,2
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LINKS
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EXAMPLE
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Triangle begins:
1;
2;
12;
192, 24;
8160, 2400;
898560, 384480, 14400;
245145600, 126040320, 9777600, 50400;
...
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MAPLE
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A001192 := proc(n) option remember: if(n=0)then return 1: fi: return add((-1)^(n-k-1)*binomial(2^k-k, n-k)*procname(k), k=0..n-1); end: A182162 := proc(n, l) local vl: vl := add((-1)^(k-l)*binomial(n, k)*binomial(k, l)*binomial(2^(n-k)-n+k, k)*k!*(n-k)!*A001192(n-k), k=l..n): if(vl = 0)then return NULL: fi: return vl: end: for n from 1 to 10 do seq(A182162(n, l), l=1..n); od; # Nathaniel Johnston, Apr 18 2012
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MATHEMATICA
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A001192[n_] := A001192[n] = If[n == 0, 1, Sum[(-1)^(n - k - 1)*Binomial[2^k - k, n - k]*A001192[k], {k, 0, n - 1}]];
A182162[n_, l_] := Module[{vl}, vl = Sum[(-1)^(k - l)* Binomial[n, k]*Binomial[k, l]*Binomial[2^(n - k) - n + k, k]*k!*(n - k)!*A001192[n - k], {k, l, n}]; If[vl == 0, Nothing, vl]];
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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