OFFSET
1,5
COMMENTS
Row sums are:
{1, 2, 4, 13, 46, 118, 275, 633, 1481, 2844, 6535}.;
Here the interior coefficients are larger than the
pascal triangle: most generalized Pascal triangles yield smaller interior
coefficients.
FORMULA
a(n,d)=If[n == 0 || n == d, 1, f[n, d]* Binomial[d, n]]; f(n,d) = Floor[1 + d*Sech[d/2 - n]].
EXAMPLE
{{1},
{1, 1},
{1, 6, 1},
{1, 9, 9, 1},
{1, 12, 30, 12, 1},
{1, 15, 50, 50, 15,1},
{1, 12, 60, 140, 60, 12, 1},
{1, 14, 63, 245, 245, 63, 14, 1},
{1, 8, 84, 336, 630, 336, 84, 8, 1},
{1, 9, 72, 336, 1008, 1008, 336, 72, 9,1},
{1, 10, 45, 360, 1470, 2772, 1470, 360, 45, 10, 1}}
MATHEMATICA
f[n_, d_] = Floor[1 + d*Sech[d/2 - n]]; a = Table[Table[If[n == 0 || n == d, 1, f[n, d]* Binomial[ d, n]], {n, 0, d}], {d, 0, 10}]; Flatten[a] Table[Apply[Plus, Table[If[n == 1 || n == d, 1, f[n, d]* Binomial[d, n]], {n, 0, d}]], {d, 0, 10}];
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula and Gary W. Adamson, May 23 2008
STATUS
approved