A174675 Sequence A154696 adjusted to leading one:t(n,m)=A154696(n,m)-A154696(n,0)+1.
1, 1, 1, 1, 60, 1, 1, 656, 656, 1, 1, 5832, 16464, 5832, 1, 1, 49496, 302486, 302486, 49496, 1, 1, 419412, 4933332, 10171944, 4933332, 419412, 1, 1, 3593036, 76425506, 280498526, 280498526, 76425506, 3593036, 1, 1, 31167600, 1157982288
Offset: 0
Examples
{1},
{1, 1},
{1, 60, 1},
{1, 656, 656, 1},
{1, 5832, 16464, 5832, 1},
{1, 49496, 302486, 302486, 49496, 1},
{1, 419412, 4933332, 10171944, 4933332, 419412, 1},
{1, 3593036, 76425506, 280498526, 280498526, 76425506, 3593036, 1},
{1, 31167600, 1157982288, 6978681888, 12117629472, 6978681888, 1157982288, 31167600, 1},
{1, 273237776, 17387745806, 164112248126, 449798124926, 449798124926, 164112248126, 17387745806, 273237776, 1},
{1, 2414712204, 260247533196, 3735760480536, 15279843395064, 23749342002264, 15279843395064, 3735760480536, 260247533196, 2414712204, 1}
Programs
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Mathematica
Clear[t, p, q, n, m, a]; p[x_, n_] = 2^n*(1 - x)^(n + 1)*LerchPhi[x, -n, 1/2]; a = Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]; p = 2; q = 3; t[n_, m_] := (p^(n - m)*q^m + p^m*q^(n - m))*a[[n + 1]][[m + 1]]; Table[Table[t[n, m] - t[n, 0] + 1, {m, 0, n}], {n, 0, 10}]; Flatten[%]
Comments