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

1, 1, 1, 1, 36, 1, 1, 296, 296, 1, 1, 1932, 4656, 1932, 1, 1, 11696, 54086, 54086, 11696, 1, 1, 69048, 556596, 1042920, 556596, 69048, 1, 1, 405236, 5406866, 16866206, 16866206, 5406866, 405236, 1, 1, 2381700, 51004320, 247754256, 404837664

Offset: 0

Author

Roger L. Bagula, Mar 26 2010

Keywords

• nonn
• tabl
• less

Comments

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

Row sums are:

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

673894929842,...

Examples

			{1},
{1, 1},
{1, 36, 1},
{1, 296, 296, 1},
{1, 1932, 4656, 1932, 1},
{1, 11696, 54086, 54086, 11696, 1},
{1, 69048, 556596, 1042920, 556596, 69048, 1},
{1, 405236, 5406866, 16866206, 16866206, 5406866, 405236, 1},
{1, 2381700, 51004320, 247754256, 404837664, 247754256, 51004320, 2381700, 1},
{1, 14050376, 473595806, 3441231326, 8491073726, 8491073726, 3441231326, 473595806, 14050376, 1},
{1, 83216400, 4357421004, 46167420504, 164067684600, 244543444824, 164067684600, 46167420504, 4357421004, 83216400, 1}
		

Crossrefs

A154690, A154692, A154693, A154964

Programs

Maple

A174673 := proc(n,m)
    A154694(n,m)-A154694(n,0)+1 ;
end proc:
seq(seq( A174673(n,m),m=0..n),n=0..10) ; # R. J. Mathar, Mar 11 2024

Mathematica

Clear[t, p, q, n, m];
p = 2; q = 3;
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}];
Table[Table[t[n, m] - t[n, 0] + 1, {m, 0, n}], {n, 0, 10}];
Flatten[%]

Formula

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