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A157151 Triangle read by rows: A(n,0)=A(n,n)=1 and A(n,k)= (5*(n-k)+1)*A(n-1,k-1) + (5*k+1)*A(n-1,k) + 5*k*(n-k)*A(n-2,k-1) for 1<=k<n. 1

%I

%S 1,1,1,1,17,1,1,123,123,1,1,769,3046,769,1,1,4655,49500,49500,4655,1,

%T 1,27981,673015,1721070,673015,27981,1,1,167947,8363421,44640435,

%U 44640435,8363421,167947,1,1,1007753,98882848,982172031,2012583870,982172031

%N Triangle read by rows: A(n,0)=A(n,n)=1 and A(n,k)= (5*(n-k)+1)*A(n-1,k-1) + (5*k+1)*A(n-1,k) + 5*k*(n-k)*A(n-2,k-1) for 1<=k<n.

%C The row sums are 1, 2, 19, 248, 4586, 108312, 3123064, 106343608, 4176709136, 185878799152, 9244524469984,...

%e 1;

%e 1, 1;

%e 1, 17, 1;

%e 1, 123, 123, 1;

%e 1, 769, 3046, 769, 1;

%e 1, 4655, 49500, 49500, 4655, 1;

%e 1, 27981, 673015, 1721070, 673015, 27981, 1;

%e 1, 167947, 8363421, 44640435, 44640435, 8363421, 167947, 1;

%e 1, 1007753, 98882848, 982172031, 2012583870, 982172031, 98882848, 1007753, 1;

%e 1, 6046599, 1135746726, 19532828674, 72264777576, 72264777576, 19532828674, 1135746726, 6046599, 1;

%p A157151 := proc(n,k)

%p option remember;

%p if k < 0 or k> n then

%p 0;

%p elif k = 0 or k = n then

%p 1;

%p else

%p (5*(n-k)+1)*procname(n-1,k-1)

%p +(5*k+1)*procname(n-1,k)

%p +5*k*(n-k)*procname(n-2,k-1) ;

%p end if;

%p end proc:

%p seq(seq(A157151(n,k),k=0..n),n=0..10) ; # _R. J. Mathar_, Feb 06 2015

%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,easy

%O 0,5

%A _Roger L. Bagula_, Feb 24 2009

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Last modified September 19 15:43 EDT 2020. Contains 337178 sequences. (Running on oeis4.)