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 A093730 Antidiagonal sums of triangle A093729, which enumerates the number of nodes in the tree of tournament sequences. 1
 1, 1, 2, 5, 18, 102, 949, 14731, 386060, 17323052, 1351157580, 185867701560, 45682244004244, 20283964291276804, 16423005586691362832, 24434416299840231799694, 67236458264587977465709983 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Related to A008934 (the number of tournament sequences). LINKS M. Cook and M. Kleber, Tournament sequences and Meeussen sequences, Electronic J. Comb. 7 (2000), #R44. MATHEMATICA T[n_, k_] := T[n, k] = If[n<0, 0, If[n==0, 1, If[k==0, 0, If[k<=n, T[n, k-1] - T[n-1, k] + T[n-1, 2*k-1] + T[n-1, 2*k], Sum[(-1)^(j-1) * Binomial[n+1, j]*T[n, k-j], {j, 1, n+1}]]]]]; a[n_] := Sum[T[n-k, k], {k, 0, n}]; Table[a[n], {n, 0, 16}] (* Jean-François Alcover, Oct 06 2016, translated from PARI *) PROG (PARI) {T(n, k)=if(n<0, 0, if(n==0, 1, if(k==0, 0, if(k<=n, T(n, k-1)-T(n-1, k)+T(n-1, 2*k-1)+T(n-1, 2*k), sum(j=1, n+1, (-1)^(j-1)*binomial(n+1, j)*T(n, k-j))))))} a(n)=sum(k=0, n, T(n-k, k)) CROSSREFS Cf. A008934, A093729. Sequence in context: A007127 A279207 A005639 * A304918 A007769 A174122 Adjacent sequences:  A093727 A093728 A093729 * A093731 A093732 A093733 KEYWORD nonn AUTHOR Paul D. Hanna, Apr 14 2004 STATUS approved

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Last modified May 12 10:17 EDT 2021. Contains 343821 sequences. (Running on oeis4.)