%I #18 May 31 2016 03:19:41

%S 1,1,1,1,10,1,1,83,41,1,1,668,1110,122,1,1,5349,25982,8210,309,1,1,

%T 42798,572367,432328,44715,714,1,1,342391,12276495,20154955,4635787,

%U 202689,1561,1,1,2739136,260203132,879857170,402100930,38001292,815680

%N 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.

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

%C 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

%H G. C. Greubel, <a href="/A166972/b166972.txt">Table of n, a(n) for n = 1..325</a>

%e 1;

%e 1, 1;

%e 1, 10, 1;

%e 1, 83, 41, 1;

%e 1, 668, 1110, 122, 1;

%e 1, 5349, 25982, 8210, 309, 1;

%e 1, 42798, 572367, 432328, 44715, 714, 1;

%e 1, 342391, 12276495, 20154955, 4635787, 202689, 1561, 1;

%e 1, 2739136, 260203132, 879857170, 402100930, 38001292, 815680, 3298, 1;

%e 1, 21913097, 5486178860, 37015708724, 31415703470, 5658628682, 260490608, 3027488, 6821, 1;

%p A166972 := proc(n,k)

%p if k = 1 or k= n then

%p 1;

%p else

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

%p end if;

%p end proc: # _R. J. Mathar_, Nov 05 2011

%t 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 *)

%Y Cf. A111577.

%K nonn,easy,tabl

%O 1,5

%A _Roger L. Bagula_, Oct 26 2009