A166972 Triangle T(n,k) read by rows: T(n,k) = (n-k+1)*T(n-1,k-1) + (3*k-2)*k*T(n-1,k), initialized by T(n,1) = T(n,n) = 1.

1, 1, 1, 1, 10, 1, 1, 83, 41, 1, 1, 668, 1110, 122, 1, 1, 5349, 25982, 8210, 309, 1, 1, 42798, 572367, 432328, 44715, 714, 1, 1, 342391, 12276495, 20154955, 4635787, 202689, 1561, 1, 1, 2739136, 260203132, 879857170, 402100930, 38001292, 815680

Offset: 1

Author

Roger L. Bagula, Oct 26 2009

Keywords

• nonn
• easy
• tabl

Comments

The row sums are: 1, 2, 12, 126, 1902, 39852, 1092924, 37613880, 1583720640, 79861657752,...

The original format of this sequence used the recursion T(n,k) = (m*n-m*k+1)*T(n-1, k-1) + (3*k-2)*(m*k-(m-1))*T(n-1, k) for varying values of m. - G. C. Greubel, May 29 2016

Examples

			1;
1, 1;
1, 10, 1;
1, 83, 41, 1;
1, 668, 1110, 122, 1;
1, 5349, 25982, 8210, 309, 1;
1, 42798, 572367, 432328, 44715, 714, 1;
1, 342391, 12276495, 20154955, 4635787, 202689, 1561, 1;
1, 2739136, 260203132, 879857170, 402100930, 38001292, 815680, 3298, 1;
1, 21913097, 5486178860, 37015708724, 31415703470, 5658628682, 260490608, 3027488, 6821, 1;
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..325

Crossrefs

Cf. A111577.

Programs

Maple

A166972 := proc(n,k)
        if k = 1 or k= n then
                1;
        else
                (n-k+1)*procname(n-1,k-1)+(3*k-2)*k*procname(n-1,k) ;
        end if;
end proc: # R. J. Mathar, Nov 05 2011

Mathematica

A[n_, 1] := 1; A[n_, n_] := 1; A[n_, k_] := (n - k + 1)*A[n - 1, k - 1] + (3*k - 2)*k*A[n - 1, k]; Flatten[ Table[A[n, k], {n, 10}, {k, n}]] (* modified by G. C. Greubel, May 29 2016 *)