cp's OEIS Frontend

A157150 Triangle T(n, k, m) = (m*(n-k) + 1)*T(n-1, k-1, m) + (m*k + 1)*T(n-1, k, m) + m*k*(n-k)*T(n-2, k-1, m) with T(n, 0, m) = T(n, n, m) = 1 and m = 4, read by rows.

%I A157150 #10 Jan 10 2022 03:06:53
%S A157150 1,1,1,1,14,1,1,87,87,1,1,460,1790,460,1,1,2333,24178,24178,2333,1,1,
%T A157150 11706,271983,693068,271983,11706,1,1,58579,2786993,14794139,14794139,
%U A157150 2786993,58579,1,1,292952,27109300,267169640,547357078,267169640,27109300,292952,1
%N A157150 Triangle T(n, k, m) = (m*(n-k) + 1)*T(n-1, k-1, m) + (m*k + 1)*T(n-1, k, m) + m*k*(n-k)*T(n-2, k-1, m) with T(n, 0, m) = T(n, n, m) = 1 and m = 4, read by rows.
%H A157150 G. C. Greubel, <a href="/A157150/b157150.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A157150 T(n, k, m) = (m*(n-k) + 1)*T(n-1, k-1, m) + (m*k + 1)*T(n-1, k, m) + m*k*(n-k)*T(n-2, k-1, m) with T(n, 0, m) = T(n, n, m) = 1 and m = 4.
%F A157150 T(n, n-k) = T(n, k).
%e A157150 Triangle begins as:
%e A157150   1;
%e A157150   1,      1;
%e A157150   1,     14,        1;
%e A157150   1,     87,       87,         1;
%e A157150   1,    460,     1790,       460,         1;
%e A157150   1,   2333,    24178,     24178,      2333,         1;
%e A157150   1,  11706,   271983,    693068,    271983,     11706,        1;
%e A157150   1,  58579,  2786993,  14794139,  14794139,   2786993,    58579,      1;
%e A157150   1, 292952, 27109300, 267169640, 547357078, 267169640, 27109300, 292952, 1;
%p A157150 A157150:= proc(n, k);
%p A157150     if k<0 or n<k then 0;
%p A157150     elif k=0 or k=n then 1;
%p A157150     else (4*n-4*k+1)*procname(n-1, k-1) + (4*k+1)*procname(n-1, k) + 4*k*(n-k)*procname(n-2, k-1);
%p A157150     end if; end proc;
%p A157150 seq(seq(A157150(n, k), k=0..n), n=0..10); # _R. J. Mathar_, Feb 06 2015
%t A157150 T[n_, k_, m_]:= T[n, k, m]= If[k==0 || k==n, 1, (m*(n-k)+1)*T[n-1,k-1,m] + (m*k+1)*T[n-1,k,m] + m*k*(n-k)*T[n-2,k-1,m]];
%t A157150 Table[T[n,k,4], {n,0,10}, {k,0,n}]//Flatten (* modified by _G. C. Greubel_, Jan 09 2022 *)
%o A157150 (Sage)
%o A157150 @CachedFunction
%o A157150 def T(n,k,m):  # A157150
%o A157150     if (k==0 or k==n): return 1
%o A157150     else: return (m*(n-k) +1)*T(n-1,k-1,m) + (m*k+1)*T(n-1,k,m) + m*k*(n-k)*T(n-2,k-1,m)
%o A157150 flatten([[T(n,k,4) for k in (0..n)] for n in (0..20)]) # _G. C. Greubel_, Jan 09 2022
%Y A157150 Cf. A007318 (m=0), A157147 (m=1), A157148 (m=2), A157149 (m=3), this sequence (m=4), A157151 (m=5).
%Y A157150 Cf. A157152, A157153, A157154, A157155, A157156, A157207, A157208, A157209, A157210, A157211, A157212, A157268, A157272, A157273, A157274, A157275.
%K A157150 nonn,tabl,easy
%O A157150 0,5
%A A157150 _Roger L. Bagula_, Feb 24 2009
%E A157150 Edited by _G. C. Greubel_, Jan 09 2022