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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

%I

%S 1,1,1,1,7,1,1,43,43,1,1,259,806,259,1,1,1555,11720,11720,1555,1,1,

%T 9331,151215,338770,151215,9331,1,1,55987,1828221,7892635,7892635,

%U 1828221,55987,1,1,335923,21286168,162474781,304389070,162474781,21286168

%N 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).

%C The row sums are:

%C {1, 2, 9, 88, 1326, 26552, 659864, 19553688, 672582816, 26333033232,

%C 1156086137664,...}.

%C What I have done here is subtract a new symmetrical part

%C to the "zero start" Sierpinski -Pascal recursion at "down two" or n-2 in my notation:

%C m*k*(n - k)*A(n - 2, k - 1, m).

%C It uses the symmetrical k*(n-k) multiplier.

%F m=5;

%F A(n,k,m)= (m*(n - k) + 1)*A(n - 1, k - 1, m) +

%F (m*k + 1)*A(n - 1, k, m) -

%F m*k*(n - k)*A(n - 2, k - 1, m).

%e {1},

%e {1, 1},

%e {1, 7, 1},

%e {1, 43, 43, 1},

%e {1, 259, 806, 259, 1},

%e {1, 1555, 11720, 11720, 1555, 1},

%e {1, 9331, 151215, 338770, 151215, 9331, 1},

%e {1, 55987, 1828221, 7892635, 7892635, 1828221, 55987, 1},

%e {1, 335923, 21286168, 162474781, 304389070, 162474781, 21286168, 335923, 1},

%e {1, 2015539, 242321986, 3094927814, 9827251276, 9827251276, 3094927814, 242321986, 2015539, 1},

%e {1, 12093235, 2721305105, 56007388880, 282818065310, 472968432602, 282818065310, 56007388880, 2721305105, 12093235, 1}

%t Clear[A, n, k, m];

%t A[n_, 0, m_] := 1;

%t A[n_, n_, m_] := 1;

%t 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];

%t Table[A[n, k, m], {m, 0, 10}, {n, 0, 10}, {k, 0, n}];

%t Table[Flatten[Table[Table[A[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 10}]

%K nonn,tabl,uned

%O 0,5

%A _Roger L. Bagula_, Feb 24 2009

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Last modified July 12 22:46 EDT 2020. Contains 335669 sequences. (Running on oeis4.)