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A074911
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Triangle generated by Pascal's rule, except begin and end the n-th row with n!.
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4
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1, 2, 2, 6, 4, 6, 24, 10, 10, 24, 120, 34, 20, 34, 120, 720, 154, 54, 54, 154, 720, 5040, 874, 208, 108, 208, 874, 5040, 40320, 5914, 1082, 316, 316, 1082, 5914, 40320, 362880, 46234, 6996, 1398, 632, 1398, 6996, 46234, 362880
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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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, 2;
6, 4, 6;
24, 10, 10, 24;
120, 34, 20, 34, 120;
720, 154, 54, 54, 154, 720;
5040, 874, 208, 108, 208, 874, 5040;
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MATHEMATICA
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T[n_, 1] := n!;
T[n_, n_] := n!;
T[n_, k_] /; 1<k<n := T[n, k] = T[n-1, k]+T[n-1, k-1];
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PROG
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(PARI) t(n, k) = {if (k<1 || k>n, return (0)); if (k==1 || k==n, return (n!)); return (t(n-1, k-1) + t(n-1, k)); }
tabl(nn) = {for (n=1, nn, for (k=1, n, print1(t(n, k), ", "); ); print(); ); } \\ Michel Marcus, May 19 2013
(Haskell)
a074911 n k = a074911_tabl !! (n-1) !! (k-1)
a074911_row n = a074911_tabl !! (n-1)
a074911_tabl = map fst $ iterate
(\(vs, w:ws) -> (zipWith (+) ([w] ++ vs) (vs ++ [w]), ws))
([1], tail a001563_list)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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