A176489 Triangle T(n,k) = A176487(n,k)+A176488(n,k)-1 read by rows 0<=k<=n.

1, 1, 1, 1, 12, 1, 1, 35, 35, 1, 1, 82, 206, 82, 1, 1, 177, 922, 922, 177, 1, 1, 368, 3599, 7284, 3599, 368, 1, 1, 751, 12917, 46923, 46923, 12917, 751, 1, 1, 1518, 43876, 264810, 468706, 264810, 43876, 1518, 1, 1, 3053, 143588, 1365740, 3931310

Offset: 0

Author

Roger L. Bagula, Apr 19 2010

Keywords

• nonn
• tabl
• easy

Comments

Row sums are 1, 2, 14, 72, 372, 2200, 15220, 121184, 1089116, 10887384, 119752404,....

The row sums s(n) seem to obey (-45*n+124)*s(n) +(45*n^2+127*n-654)*s(n-1) +(-206*n^2+227*n+708)*s(n-2) +(303*n^2-869*n+458)*s(n-3) -2*(71*n-125)*(n-2)*s(n-4)=0. - R. J. Mathar, Jun 16 2015

Examples

			1;
1, 1;
1, 12, 1;
1, 35, 35, 1;
1, 82, 206, 82, 1;
1, 177, 922, 922, 177, 1;
1, 368, 3599, 7284, 3599, 368, 1;
1, 751, 12917, 46923, 46923, 12917, 751, 1;
1, 1518, 43876, 264810, 468706, 264810, 43876, 1518, 1;
1, 3053, 143588, 1365740, 3931310, 3931310, 1365740, 143588, 3053, 1;
1, 6124, 457997, 6610700, 29214758, 47173244, 29214758, 6610700, 457997, 6124, 1;
		

Crossrefs

Cf. A007318, A008292.

Programs

Maple

A176489 := proc(n,k)
    A176487(n,k)+A176488(n,k)-1 ;
end proc: # R. J. Mathar, Jun 16 2015

Mathematica

<< DiscreteMath`Combinatorica`;
t[n_, m_, 0] := Binomial[n, m];
t[n_, m_, 1] := Eulerian[1 + n, m];
t[n_, m_, q_] := t[n, m, q] = t[n, m, q - 1] + t[n, m, q - 2] - 1;
Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 0, 10}]