A174674 Sequence A154695 adjusted to leading one:t(n,m)=A154695(n,m)-A154695(n,0)+1

1, 1, 1, 1, 20, 1, 1, 130, 130, 1, 1, 744, 1824, 744, 1, 1, 4234, 20152, 20152, 4234, 1, 1, 24484, 210796, 376704, 210796, 24484, 1, 1, 143686, 2183524, 6233224, 6233224, 2183524, 143686, 1, 1, 851504, 22549360, 99411264, 149600192, 99411264

Offset

0,5

Comments

Row sums are:

1, 2, 22, 262, 3314, 48774, 847266, 17120870, 395224450, 10263445126,

296140564130,...

Links

Table of n, a(n) for n=0..41.

Formula

t(n,m)=A154695(n,m)-A154695(n,0)+1

Example

{1},
{1, 1},
{1, 20, 1},
{1, 130, 130, 1},
{1, 744, 1824, 744, 1},
{1, 4234, 20152, 20152, 4234, 1},
{1, 24484, 210796, 376704, 210796, 24484, 1},
{1, 143686, 2183524, 6233224, 6233224, 2183524, 143686, 1},
{1, 851504, 22549360, 99411264, 149600192, 99411264, 22549360, 851504, 1},
{1, 5075122, 231836368, 1562973472, 3331837600, 3331837600, 1562973472, 231836368, 5075122, 1},
{1, 30344508, 2370195636, 24248921920, 72553861536, 97733916928, 72553861536, 24248921920, 2370195636, 30344508, 1}

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 = 1;
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[%]

Crossrefs

A154690, A154692, A154693, A154694, A154695

Sequence in context: A139459 A154652 A155516 * A144443 A257608 A022183

Adjacent sequences: A174671 A174672 A174673 * A174675 A174676 A174677

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 26 2010

Status

approved