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 A173003 Antidiagonal triangle sequence based on recursion: f(n,a)=a*n*f(n-1,a)+f(n-2,a) 0
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Row sums are: {0, 1, 3, 12, 62, 425, 3811, 43714, 624536, 10826503,...}. LINKS FORMULA f(n,a)=a*n*f(n-1,a)+f(n-2,a); t(n,m)=antidiagonal(f(n,a)) EXAMPLE {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} MATHEMATICA 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[%] CROSSREFS Sequence in context: A106579 A287318 A329020 * A335461 A294411 A274390 Adjacent sequences:  A173000 A173001 A173002 * A173004 A173005 A173006 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Feb 07 2010 STATUS approved

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Last modified August 3 11:54 EDT 2020. Contains 336198 sequences. (Running on oeis4.)