A174802 Triangular sequence from antidiagonal expansion of: p(x,m) = x*(x + 1)^(m - 1)/(1 - Sum[x^i, {i, 1, m}]).

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 5, 5, 4, 1, 1, 8, 9, 8, 5, 1, 1, 13, 17, 14, 12, 6, 1, 1, 21, 31, 27, 22, 17, 7, 1, 1, 34, 57, 53, 41, 34, 23, 8, 1

Offset

1,5

Comments

Row sums are {1, 2, 4, 8, 16, 32, 64, 127, 252, ...}.

Links

Table of n, a(n) for n=1..45.

Formula

p(x,m) = x*(x + 1)^(m - 1)/(1 - Sum[x^i, {i, 1, m}]);

t(n,m) = antidiagonal(expansion(p,x,n))).

Example

{1},
{1, 1},
{1, 2, 1},
{1, 3, 3, 1},
{1, 5, 5, 4, 1},
{1, 8, 9, 8, 5, 1},
{1, 13, 17, 14, 12, 6, 1},
{1, 21, 31, 27, 22, 17, 7, 1},
{1, 34, 57, 53, 41, 34, 23, 8, 1}

Mathematica

p[x_, m_] = x*(x + 1)^(m - 1)/(1 - Sum[x^i, {i, 1, m}])
a = Table[Table[SeriesCoefficient[Series[FullSimplify[ExpandAll[ p[x, m]]], {x, 0, 50}], n], {n, 0, 10}], {m, 1, 10}]
Table[Table[a[[m, n - m + 1]], {m, 1, n - 1}], {n, 2, 10}]
Flatten[%]
Table[Sum[a[[m, n - m + 1]], {m, 1, n - 1}], {n, 2, 10}]

Crossrefs

Sequence in context: A054450 A344610 A337009 * A238346 A053538 A235803

Adjacent sequences: A174799 A174800 A174801 * A174803 A174804 A174805

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 29 2010

Status

approved