1,3

Row sums are:

{1, 2, 6, 26, 150, 1082, 9366, 94586, 1091670, 14174522, 204495126}.

This sequence is just a substitution of : x->m*x.

Triangle T(n,k), 0<=k<=n, read by rows given by [0,1,0,2,0,3,0,4,0,5,0,6,...] DELTA [2,0,4,0,6,0,8,0,10,0,...] where DELTA is the operator defined in A084938 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 15 2008]

m=2; f(x, n) = (1 - m*x)^(n + 1)*Sum[k^n*(m*x)^k, {k, 0, Infinity}]; t(n,m)=Coefficients(f(x,n)).

T(n,k)=2^k*A123125(n,k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 15 2008]

{1},

{0, 2},

{0, 2, 4},

{0, 2, 16, 8},

{0, 2, 44, 88, 16},

{0, 2, 104, 528, 416, 32},

{0, 2, 228, 2416, 4832, 1824, 64},

{0, 2, 480, 9528, 38656, 38112, 7680, 128},

{0, 2, 988, 34344, 249904, 499808, 274752, 31616, 256},

{0, 2, 2008, 116864, 1411744, 4998080, 5646976, 1869824, 128512, 512},

{0, 2, 4052, 382720, 7283072, 41931328, 83862656, 58264576, 12247040, 518656, 1024}

Clear[f, x, n, a, m] m = 2; f[x_, n_] := f[x, n] = (1 - m*x)^(n + 1)*Sum[k^n*(m*x)^k, {k, 0, Infinity}] Table[FullSimplify[ExpandAll[f[x, n]]], {n, 0, 10}]; a = Table[CoefficientList[FullSimplify[ExpandAll[f[x, n]]], x], {n, 0, 10}]; Flatten[a]

Cf. A123125.

Sequence in context: A136716 A117946 A061930 this_sequence A115273 A126440 A131186

Adjacent sequences: A141657 A141658 A141659 this_sequence A141661 A141662 A141663

nonn,uned

Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Sep 04 2008

Corrected example . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 16 2008