A174673 - OEIS

%I #5 Mar 11 2024 06:50:21

%S 1,1,1,1,36,1,1,296,296,1,1,1932,4656,1932,1,1,11696,54086,54086,

%T 11696,1,1,69048,556596,1042920,556596,69048,1,1,405236,5406866,

%U 16866206,16866206,5406866,405236,1,1,2381700,51004320,247754256,404837664

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

%C Reduces the values in the triangle A154694 such that each row starts with 1.

%C Row sums are:

%C 1, 2, 38, 594, 8522, 131566, 2294210, 45356618, 1007118218, 24839902470,

%C 673894929842,...

%F t(n,m)=A154694(n,m)-A154694(n,0)+1

%e {1},

%e {1, 1},

%e {1, 36, 1},

%e {1, 296, 296, 1},

%e {1, 1932, 4656, 1932, 1},

%e {1, 11696, 54086, 54086, 11696, 1},

%e {1, 69048, 556596, 1042920, 556596, 69048, 1},

%e {1, 405236, 5406866, 16866206, 16866206, 5406866, 405236, 1},

%e {1, 2381700, 51004320, 247754256, 404837664, 247754256, 51004320, 2381700, 1},

%e {1, 14050376, 473595806, 3441231326, 8491073726, 8491073726, 3441231326, 473595806, 14050376, 1},

%e {1, 83216400, 4357421004, 46167420504, 164067684600, 244543444824, 164067684600, 46167420504, 4357421004, 83216400, 1}

%p A174673 := proc(n,m)

%p     A154694(n,m)-A154694(n,0)+1 ;

%p end proc:

%p seq(seq( A174673(n,m),m=0..n),n=0..10) ; # _R. J. Mathar_, Mar 11 2024

%t Clear[t, p, q, n, m];

%t p = 2; q = 3;

%t 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 Table[Table[t[n, m] - t[n, 0] + 1, {m, 0, n}], {n, 0, 10}];

%t Flatten[%]

%Y A154690, A154692, A154693, A154964

%K nonn,tabl,less

%O 0,5

%A _Roger L. Bagula_, Mar 26 2010