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A157150 Triangle read by rows: A(n,0)=A(n,n)=1 and A(n,k)= (4*(n-k)+1)*A(n-1,k-1) + (4*k+1)*A(n-1,k) + 4*k*(n-k)*A(n-2,k-1) for 1<=k<n. 1
1, 1, 1, 1, 14, 1, 1, 87, 87, 1, 1, 460, 1790, 460, 1, 1, 2333, 24178, 24178, 2333, 1, 1, 11706, 271983, 693068, 271983, 11706, 1, 1, 58579, 2786993, 14794139, 14794139, 2786993, 58579, 1, 1, 292952, 27109300, 267169640, 547357078, 267169640 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The row sums are 1, 2, 16, 176, 2712, 53024, 1260448, 35279424, 1136500864, 41415979520, 1684431360768,...

LINKS

Table of n, a(n) for n=0..41.

EXAMPLE

1;

1, 1;

1, 14, 1;

1, 87, 87, 1;

1, 460, 1790, 460, 1;

1, 2333, 24178, 24178, 2333, 1;

1, 11706, 271983, 693068, 271983, 11706, 1;

1, 58579, 2786993, 14794139, 14794139, 2786993, 58579, 1;

1, 292952, 27109300, 267169640, 547357078, 267169640, 27109300, 292952, 1;

1, 1464825, 255759732, 4351601316, 16099163886, 16099163886, 4351601316, 255759732, 1464825, 1;

MAPLE

A157150 := proc(n, k)

    option remember;

    if k < 0 or k> n then

        0;

    elif k = 0 or k = n then

        1;

    else

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

        +(4*k+1)*procname(n-1, k)

        +4*k*(n-k)*procname(n-2, k-1) ;

    end if;

end proc:

seq(seq(A157150(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: A157633 A157278 A144441 * A142461 A174720 A060628

Adjacent sequences:  A157147 A157148 A157149 * A157151 A157152 A157153

KEYWORD

nonn,tabl,easy

AUTHOR

Roger L. Bagula, Feb 24 2009

STATUS

approved

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Last modified September 27 18:13 EDT 2020. Contains 337386 sequences. (Running on oeis4.)