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A174673 Triangle read by rows: T(n,m)=A154694(n,m)-A154694(n,0)+1.

%I A174673 #5 Mar 11 2024 06:50:21
%S A174673 1,1,1,1,36,1,1,296,296,1,1,1932,4656,1932,1,1,11696,54086,54086,
%T A174673 11696,1,1,69048,556596,1042920,556596,69048,1,1,405236,5406866,
%U A174673 16866206,16866206,5406866,405236,1,1,2381700,51004320,247754256,404837664
%N A174673 Triangle read by rows: T(n,m)=A154694(n,m)-A154694(n,0)+1.
%C A174673 Reduces the values in the triangle A154694 such that each row starts with 1.
%C A174673 Row sums are:
%C A174673 1, 2, 38, 594, 8522, 131566, 2294210, 45356618, 1007118218, 24839902470,
%C A174673 673894929842,...
%F A174673 t(n,m)=A154694(n,m)-A154694(n,0)+1
%e A174673 {1},
%e A174673 {1, 1},
%e A174673 {1, 36, 1},
%e A174673 {1, 296, 296, 1},
%e A174673 {1, 1932, 4656, 1932, 1},
%e A174673 {1, 11696, 54086, 54086, 11696, 1},
%e A174673 {1, 69048, 556596, 1042920, 556596, 69048, 1},
%e A174673 {1, 405236, 5406866, 16866206, 16866206, 5406866, 405236, 1},
%e A174673 {1, 2381700, 51004320, 247754256, 404837664, 247754256, 51004320, 2381700, 1},
%e A174673 {1, 14050376, 473595806, 3441231326, 8491073726, 8491073726, 3441231326, 473595806, 14050376, 1},
%e A174673 {1, 83216400, 4357421004, 46167420504, 164067684600, 244543444824, 164067684600, 46167420504, 4357421004, 83216400, 1}
%p A174673 A174673 := proc(n,m)
%p A174673     A154694(n,m)-A154694(n,0)+1 ;
%p A174673 end proc:
%p A174673 seq(seq( A174673(n,m),m=0..n),n=0..10) ; # _R. J. Mathar_, Mar 11 2024
%t A174673 Clear[t, p, q, n, m];
%t A174673 p = 2; q = 3;
%t A174673 t[n_, m_] = (p^(n - m)*q^m + p^m*q^( n - m))*Sum[(-1)^j*Binomial[n + 2, j]*(m - j + 1)^(n + 1), {j, 0, m + 1}];
%t A174673 Table[Table[t[n, m] - t[n, 0] + 1, {m, 0, n}], {n, 0, 10}];
%t A174673 Flatten[%]
%Y A174673 A154690, A154692, A154693, A154964
%K A174673 nonn,tabl,less
%O A174673 0,5
%A A174673 _Roger L. Bagula_, Mar 26 2010