A176791 Triangle t(n,m) read by rows: t(n,m) = binomial(2^n-1, 2^m-1) if n >= 2*m, otherwise symmetrically extended t(n,m) = t(n,n-m).

1, 1, 1, 1, 3, 1, 1, 7, 7, 1, 1, 15, 455, 15, 1, 1, 31, 4495, 4495, 31, 1, 1, 63, 39711, 553270671, 39711, 63, 1, 1, 127, 333375, 89356415775, 89356415775, 333375, 127, 1, 1, 255, 2731135, 12801990477375, 629921975126394617164575, 12801990477375

Offset

0,5

Comments

Row sums are 1, 2, 5, 16, 487, 9054, 553350221, 178713498556, 629921975151998603582107, 52571341051325843383483521914, ...

Links

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

Example

1;
1, 1;
1, 3, 1;
1, 7, 7, 1;
1, 15, 455, 15, 1;
1, 31, 4495, 4495, 31, 1;
1, 63, 39711, 553270671, 39711, 63, 1;
1, 127, 333375, 89356415775, 89356415775, 333375, 127, 1;
1, 255, 2731135, 12801990477375, 629921975126394617164575, 12801990477375, 2731135, 255, 1

Maple

A176791 := proc(n, m)
        if n >= 2*m then
                binomial(2^n-1, 2^m-1) ;
        else
                procname(n, n-m) ;
        end if:
end proc: # R. J. Mathar, Jan 29 2012

Mathematica

t[n_, m_] := If[Floor[n/2] >= m, Binomial[2^n - 1, 2^m - 1], Binomial[2^n - 1, 2^(n - m) - 1]];
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Cf. A174387.

Sequence in context: A057004 A059328 A174387 * A259471 A220555 A369559

Adjacent sequences: A176788 A176789 A176790 * A176792 A176793 A176794

Keyword

nonn,tabl,easy

Author

Roger L. Bagula, Apr 26 2010

Status

approved