A176491 Triangle T(n,k) = binomial(n,k) + A176490(n,k) - 1 read along rows 0<=k<=n.

1, 1, 1, 1, 10, 1, 1, 35, 35, 1, 1, 104, 300, 104, 1, 1, 297, 1992, 1992, 297, 1, 1, 846, 11747, 25982, 11747, 846, 1, 1, 2431, 64969, 275375, 275375, 64969, 2431, 1, 1, 7060, 346246, 2573576, 4831272, 2573576, 346246, 7060, 1, 1, 20693, 1804214, 22163246

Offset: 0

Author

Roger L. Bagula, Apr 19 2010

Keywords

• nonn
• tabl
• easy

Comments

Row sums are 1, 2, 12, 72, 510, 4580, 51170, 685552, 10685038, 189423852, 3755809002,....

Examples

			1;
1, 1;
1, 10, 1;
1, 35, 35, 1;
1, 104, 300, 104, 1;
1, 297, 1992, 1992, 297, 1;
1, 846, 11747, 25982, 11747, 846, 1;
1, 2431, 64969, 275375, 275375, 64969, 2431, 1;
1, 7060, 346246, 2573576, 4831272, 2573576, 346246, 7060, 1;
1, 20693, 1804214, 22163246, 70723772, 70723772, 22163246, 1804214, 20693, 1;
1, 61082, 9268821, 180504510, 916661604, 1542816966, 916661604, 180504510, 9268821, 61082, 1;
		

Crossrefs

Cf. A007318, A008292, A060187, A176487.

Programs

Maple

A176491 := proc(n,k)
        A176490(n,k)+binomial(n,k)-1 ;
end proc: # R. J. Mathar, Jun 16 2015

Mathematica

(*A060187*)
p[x_, n_] = (1 - x)^(n + 1)*Sum[(2*k + 1)^n*x^k, {k, 0, Infinity}];
f[n_, m_] := CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x][[m + 1]];
<< DiscreteMath`Combinatorica`;
t[n_, m_, 0] := Binomial[n, m];
t[n_, m_, 1] := Eulerian[1 + n, m];
t[n_, m_, 2] := f[n, m];
t[n_, m_, q_] := t[n, m, q] = t[n, m, q - 2] + t[n, m, q - 3] - 1;
Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 0, 10}]