A176492 Triangle T(n,k) = A176492(n,k) + A008292(n+1,k+1) - 1 read along rows 0<=k<=n.

1, 1, 1, 1, 13, 1, 1, 45, 45, 1, 1, 129, 365, 129, 1, 1, 353, 2293, 2293, 353, 1, 1, 965, 12937, 28397, 12937, 965, 1, 1, 2677, 69261, 290993, 290993, 69261, 2677, 1, 1, 7561, 360853, 2661809, 4987461, 2661809, 360853, 7561, 1, 1, 21705, 1852053, 22618437

Offset

0,5

Comments

Row sums are 1, 2, 15, 92, 625, 5294, 56203, 725864, 11047909, 193052642, 3795725791,....

Links

Table of n, a(n) for n=0..48.

Example

1;
1, 1;
1, 13, 1;
1, 45, 45, 1;
1, 129, 365, 129, 1;
1, 353, 2293, 2293, 353, 1;
1, 965, 12937, 28397, 12937, 965, 1;
1, 2677, 69261, 290993, 290993, 69261, 2677, 1;
1, 7561, 360853, 2661809, 4987461, 2661809, 360853, 7561, 1;
, 21705, 1852053, 22618437, 72034125, 72034125, 22618437, 1852053, 21705, 1;
1, 63117, 9421457, 182707997, 926399717, 1558541213, 926399717, 182707997, 9421457, 63117, 1;

Maple

A176492 := proc(n, k)
    A176491(n, k)+A008292(n+1, k+1)-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}]

Crossrefs

Cf. A007318, A008292, A060187, A176487.

Sequence in context: A141596 A108477 A176204 * A174731 A342891 A174694

Adjacent sequences: A176489 A176490 A176491 * A176493 A176494 A176495

Keyword

nonn,tabl,easy

Author

Roger L. Bagula, Apr 19 2010

Status

approved