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A350487
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Triangle read by rows: T(n,k) is the number of acyclic digraphs on n labeled nodes with k arcs and a global source, n >= 1, k = 0..n*(n-1)/2.
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3
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1, 0, 2, 0, 0, 9, 6, 0, 0, 0, 64, 132, 96, 24, 0, 0, 0, 0, 625, 2640, 4850, 4900, 2850, 900, 120, 0, 0, 0, 0, 0, 7776, 55800, 186480, 379170, 516660, 491040, 328680, 152640, 46980, 8640, 720, 0, 0, 0, 0, 0, 0, 117649, 1286670, 6756120, 22466010
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listen;
history;
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internal format)
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OFFSET
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1,3
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LINKS
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EXAMPLE
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Triangle begins:
[1] 1;
[2] 0, 2;
[3] 0, 0, 9, 6;
[4] 0, 0, 0, 64, 132, 96, 24;
[5] 0, 0, 0, 0, 625, 2640, 4850, 4900, 2850, 900, 120;
...
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PROG
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(PARI)
T(n)={my(a=vector(n)); a[1]=1; for(n=2, #a, a[n]=sum(k=1, n-1, (-1)^(k-1)*binomial(n, k)*((1+'y)^(n-k)-1)^k*a[n-k])); [Vecrev(p) | p <- a]}
{ my(A=T(6)); for(n=1, #A, print(A[n])) }
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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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STATUS
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approved
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