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A157149 Triangle read by rows: A(n,0)=A(n,n)=1 and A(n,k)= (3*(n-k)+1)*A(n-1,k-1) + (3*k+1)*A(n-1,k) + 3*k*(n-k)*A(n-2,k-1) for 1<=k<n. 1
1, 1, 1, 1, 11, 1, 1, 57, 57, 1, 1, 247, 930, 247, 1, 1, 1013, 10006, 10006, 1013, 1, 1, 4083, 89139, 225230, 89139, 4083, 1, 1, 16369, 719691, 3771323, 3771323, 719691, 16369, 1, 1, 65519, 5495836, 53239541, 108865438, 53239541, 5495836, 65519, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The row sums are: 1, 2, 13, 116, 1426, 22040, 411676, 9014768, 226467232, 6419808464, 202704612424,...

LINKS

Table of n, a(n) for n=0..45.

EXAMPLE

1;

1, 1;

1, 11, 1;

1, 57, 57, 1;

1, 247, 930, 247, 1;

1, 1013, 10006, 10006, 1013, 1;

1, 4083, 89139, 225230, 89139, 4083, 1;

1, 16369, 719691, 3771323, 3771323, 719691, 16369, 1;

1, 65519, 5495836, 53239541, 108865438, 53239541, 5495836, 65519, 1;

1, 262125, 40599768, 675679608, 2493362730, 2493362730, 675679608, 40599768, 262125, 1;

MAPLE

A157149 := proc(n, k)

    option remember;

    if k < 0 or k> n then

        0;

    elif k = 0 or k = n then

        1;

    else

        (3*(n-k)+1)*procname(n-1, k-1)

        +(3*k+1)*procname(n-1, k)

        +3*k*(n-k)*procname(n-2, k-1) ;

    end if;

end proc:

seq(seq(A157149(n, k), k=0..n), n=0..10) ; # R. J. Mathar, Feb 06 2015

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: A144440 A157209 A014469 * A166979 A022174 A173006

Adjacent sequences:  A157146 A157147 A157148 * A157150 A157151 A157152

KEYWORD

nonn,tabl,easy

AUTHOR

Roger L. Bagula, Feb 24 2009

STATUS

approved

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Last modified September 30 03:19 EDT 2020. Contains 337432 sequences. (Running on oeis4.)