A174672 Sequence A154693 adjusted to leading one:t(n,m)=A154693(n,m)-A154693(n,0)+1

1, 1, 1, 1, 12, 1, 1, 58, 58, 1, 1, 244, 512, 244, 1, 1, 994, 3592, 3592, 994, 1, 1, 4016, 23756, 38592, 23756, 4016, 1, 1, 16174, 154420, 374728, 374728, 154420, 16174, 1, 1, 65004, 993088, 3529104, 4997824, 3529104, 993088, 65004, 1, 1, 260842, 6314368

Offset

0,5

Comments

Row sums are:

1, 2, 14, 118, 1002, 9174, 94138, 1090646, 14172218, 204490006, 3245253882,...

Links

Table of n, a(n) for n=0..47.

Formula

t(n,m)=A154693(n,m)-A154693(n,0)+1

Example

{1},
{1, 1},
{1, 12, 1},
{1, 58, 58, 1},
{1, 244, 512, 244, 1},
{1, 994, 3592, 3592, 994, 1},
{1, 4016, 23756, 38592, 23756, 4016, 1},
{1, 16174, 154420, 374728, 374728, 154420, 16174, 1},
{1, 65004, 993088, 3529104, 4997824, 3529104, 993088, 65004, 1},
{1, 260842, 6314368, 32773312, 62896480, 62896480, 32773312, 6314368, 260842, 1},
{1, 1045480, 39684596, 299673344, 779048096, 1006350848, 779048096, 299673344, 39684596, 1045480, 1}

Mathematica

Clear[t, p, q, n, m];
p = 2; q = 1;
t[n_, m_] = (p^(n - m)*q^m + p^m*q^( n - m))*Sum[(-1)^j*Binomial[n + 2, j]*(m - j + 1)^(n + 1), {j, 0, m + 1}];
Table[Table[t[n, m] - t[n, 0] + 1, {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

A154690, A154692, A154693

Sequence in context: A350729 A168518 A174667 * A174151 A342890 A155491

Adjacent sequences: A174669 A174670 A174671 * A174673 A174674 A174675

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 26 2010

Status

approved