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A173003
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Antidiagonal triangle sequence based on recursion: f(n,a)=a*n*f(n-1,a)+f(n-2,a)
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0
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0, 0, 1, 0, 1, 2, 0, 1, 4, 7, 0, 1, 6, 25, 30, 0, 1, 8, 55, 204, 157, 0, 1, 10, 97, 666, 2065, 972, 0, 1, 12, 151, 1560, 10045, 24984, 6961, 0, 1, 14, 217, 3030, 31297, 181476, 351841, 56660, 0, 1, 16, 295, 5220, 75901, 752688, 3821041, 5654440, 516901
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OFFSET
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0,6
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COMMENTS
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Row sums are:
{0, 1, 3, 12, 62, 425, 3811, 43714, 624536, 10826503,...}.
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LINKS
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Table of n, a(n) for n=0..54.
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FORMULA
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f(n,a)=a*n*f(n-1,a)+f(n-2,a);
t(n,m)=antidiagonal(f(n,a))
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EXAMPLE
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{0},
{0, 1},
{0, 1, 2},
{0, 1, 4, 7},
{0, 1, 6, 25, 30},
{0, 1, 8, 55, 204, 157},
{0, 1, 10, 97, 666, 2065, 972},
{0, 1, 12, 151, 1560, 10045, 24984, 6961},
{0, 1, 14, 217, 3030, 31297, 181476, 351841, 56660},
{0, 1, 16, 295, 5220, 75901, 752688, 3821041, 5654440, 516901}
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MATHEMATICA
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f[0, a_] := 0; f[1, a_] := 1;
f[n_, a_] := f[n, a] = a*n*f[n - 1, a] + f[n - 2, a];
m1 = Table[f[n, a], {n, 0, 10}, {a, 1, 11}];
Table[Table[m1[[m, n - m + 1]], {m, 1, n}], {n, 1, 10}];
Flatten[%]
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CROSSREFS
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Sequence in context: A106579 A287318 A329020 * A335461 A294411 A274390
Adjacent sequences: A173000 A173001 A173002 * A173004 A173005 A173006
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula, Feb 07 2010
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STATUS
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approved
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