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 A157156 A general three part recursion triangle sequence second type: m=5; A(n,k,m)= (m*(n - k) + 1)*A(n - 1, k - 1, m) + (m*k + 1)*A(n - 1, k, m) - m*k*(n - k)*A(n - 2, k - 1, m). 0
 1, 1, 1, 1, 7, 1, 1, 43, 43, 1, 1, 259, 806, 259, 1, 1, 1555, 11720, 11720, 1555, 1, 1, 9331, 151215, 338770, 151215, 9331, 1, 1, 55987, 1828221, 7892635, 7892635, 1828221, 55987, 1, 1, 335923, 21286168, 162474781, 304389070, 162474781, 21286168 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS The row sums are: {1, 2, 9, 88, 1326, 26552, 659864, 19553688, 672582816, 26333033232, 1156086137664,...}. What I have done here is subtract a new symmetrical part to the "zero start" Sierpinski -Pascal recursion at "down two" or n-2 in my notation: m*k*(n - k)*A(n - 2, k - 1, m). It uses the symmetrical k*(n-k) multiplier. LINKS FORMULA m=5; A(n,k,m)= (m*(n - k) + 1)*A(n - 1, k - 1, m) + (m*k + 1)*A(n - 1, k, m) - m*k*(n - k)*A(n - 2, k - 1, m). EXAMPLE {1}, {1, 1}, {1, 7, 1}, {1, 43, 43, 1}, {1, 259, 806, 259, 1}, {1, 1555, 11720, 11720, 1555, 1}, {1, 9331, 151215, 338770, 151215, 9331, 1}, {1, 55987, 1828221, 7892635, 7892635, 1828221, 55987, 1}, {1, 335923, 21286168, 162474781, 304389070, 162474781, 21286168, 335923, 1}, {1, 2015539, 242321986, 3094927814, 9827251276, 9827251276, 3094927814, 242321986, 2015539, 1}, {1, 12093235, 2721305105, 56007388880, 282818065310, 472968432602, 282818065310, 56007388880, 2721305105, 12093235, 1} MATHEMATICA Clear[A, n, k, m]; A[n_, 0, m_] := 1; A[n_, n_, m_] := 1; A[n_, k_, m_] := (m*(n - k) + 1)*A[n - 1, k - 1, m] + (m* k + 1)*A[n - 1, k, m] - m*k*(n - k)*A[n - 2, k - 1, m]; Table[A[n, k, m], {m, 0, 10}, {n, 0, 10}, {k, 0, n}]; Table[Flatten[Table[Table[A[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 10}] CROSSREFS Sequence in context: A156916 A173584 A166973 * A022170 A178658 A156602 Adjacent sequences:  A157153 A157154 A157155 * A157157 A157158 A157159 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Feb 24 2009 STATUS approved

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Last modified May 29 20:42 EDT 2020. Contains 334710 sequences. (Running on oeis4.)