A176488 Triangle T(n,k) = A008292(n+1,k+1) + A176487(n,k) - 1, 0<=k<=n.

1, 1, 1, 1, 8, 1, 1, 23, 23, 1, 1, 54, 136, 54, 1, 1, 117, 612, 612, 117, 1, 1, 244, 2395, 4850, 2395, 244, 1, 1, 499, 8605, 31271, 31271, 8605, 499, 1, 1, 1010, 29242, 176522, 312448, 176522, 29242, 1010, 1, 1, 2033, 95714, 910466, 2620832, 2620832, 910466

Offset: 0

Author

Roger L. Bagula, Apr 19 2010

Keywords

• nonn
• tabl
• easy

Comments

Row sums are 1, 2, 10, 48, 246, 1460, 10130, 80752, 725998, 7258092, 79834602,....

Apparently the row sums 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, 8, 1;
1, 23, 23, 1;
1, 54, 136, 54, 1;
1, 117, 612, 612, 117, 1;
1, 244, 2395, 4850, 2395, 244, 1;
1, 499, 8605, 31271, 31271, 8605, 499, 1;
1, 1010, 29242, 176522, 312448, 176522, 29242, 1010, 1;
1, 2033, 95714, 910466, 2620832, 2620832, 910466, 95714, 2033, 1;
1, 4080, 305317, 4407094, 19476436, 31448746, 19476436, 4407094, 305317, 4080, 1;
		

Crossrefs

Cf. A007318, A008292.

Programs

Maple

A176488 := proc(n,k)
    A008292(n+1,k+1)+A176487(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}]