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A157148 Triangle read by rows: A(n,0)=A(n,n)=1 and A(n,k)= (2*(n-k)+1)*A(n-1,k-1) + (2*k+1)*A(n-1,k) + 2*k*(n-k)*A(n-2,k-1) for 1<=k<n. 1
1, 1, 1, 1, 8, 1, 1, 33, 33, 1, 1, 112, 394, 112, 1, 1, 353, 3150, 3150, 353, 1, 1, 1080, 20719, 51192, 20719, 1080, 1, 1, 3265, 122535, 620415, 620415, 122535, 3265, 1, 1, 9824, 681040, 6312360, 12805614, 6312360, 681040, 9824, 1, 1, 29505, 3643980 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The row sums are 1, 2, 10, 68, 620, 7008, 94792, 1492432, 26812064, 541255744, 12129218272,....

LINKS

Table of n, a(n) for n=0..47.

EXAMPLE

1;

1, 1;

1, 8, 1;

1, 33, 33, 1;

1, 112, 394, 112, 1;

1, 353, 3150, 3150, 353, 1;

1, 1080, 20719, 51192, 20719, 1080, 1;

1, 3265, 122535, 620415, 620415, 122535, 3265, 1;

1, 9824, 681040, 6312360, 12805614, 6312360, 681040, 9824, 1;

1, 29505, 3643980, 57451300, 209503086, 209503086, 57451300, 3643980, 29505, 1;

MAPLE

A157148 := proc(n, k)

    option remember;

    if k < 0 or k> n then

        0;

    elif k = 0 or k = n then

        1;

    else

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

        +(2*k+1)*procname(n-1, k)

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

    end if;

end proc:

seq(seq(A157148(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: A178347 A141686 A185412 * A220595 A154335 A142467

Adjacent sequences:  A157145 A157146 A157147 * A157149 A157150 A157151

KEYWORD

nonn,tabl,easy

AUTHOR

Roger L. Bagula, Feb 24 2009

STATUS

approved

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Last modified September 26 16:43 EDT 2020. Contains 337374 sequences. (Running on oeis4.)