A176492 - OEIS

%I #10 Jun 17 2015 04:04:43

%S 1,1,1,1,13,1,1,45,45,1,1,129,365,129,1,1,353,2293,2293,353,1,1,965,

%T 12937,28397,12937,965,1,1,2677,69261,290993,290993,69261,2677,1,1,

%U 7561,360853,2661809,4987461,2661809,360853,7561,1,1,21705,1852053,22618437

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

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

%e 1;

%e 1, 1;

%e 1, 13, 1;

%e 1, 45, 45, 1;

%e 1, 129, 365, 129, 1;

%e 1, 353, 2293, 2293, 353, 1;

%e 1, 965, 12937, 28397, 12937, 965, 1;

%e 1, 2677, 69261, 290993, 290993, 69261, 2677, 1;

%e 1, 7561, 360853, 2661809, 4987461, 2661809, 360853, 7561, 1;

%e , 21705, 1852053, 22618437, 72034125, 72034125, 22618437, 1852053, 21705, 1;

%e 1, 63117, 9421457, 182707997, 926399717, 1558541213, 926399717, 182707997, 9421457, 63117, 1;

%p A176492 := proc(n,k)

%p     A176491(n,k)+A008292(n+1,k+1)-1 ;

%p end proc: # _R. J. Mathar_, Jun 16 2015

%t (*A060187*)

%t p[x_, n_] = (1 - x)^(n + 1)*Sum[(2*k + 1)^n*x^k, {k, 0, Infinity}];

%t f[n_, m_] := CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x][[m + 1]];

%t << DiscreteMath`Combinatorica`;

%t t[n_, m_, 0] := Binomial[n, m];

%t t[n_, m_, 1] := Eulerian[1 + n, m];

%t t[n_, m_, 2] := f[n, m];

%t t[n_, m_, q_] := t[n, m, q] = t[n, m, q - 2] + t[n, m, q - 3] - 1;

%t Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 0, 10}]

%Y Cf. A007318, A008292, A060187, A176487.

%K nonn,tabl,easy

%O 0,5

%A _Roger L. Bagula_, Apr 19 2010