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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

Table of n, a(n) for n=0..42.

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.)