OFFSET
1,6
COMMENTS
Row sums are:
{0, 2, 6, 16, 38, 86, 188, 402, 846, 1760, 3630}.
The odd n row are the most interesting.
The function was abstracted from the Mathematica generating function for
A052509 by taking out the powers of two:
t(n,m)=(n - m)!*(2^(-m + n)/Gamma[1 - m + n] - Hypergeometric2F1[1, 1 + 2 m - n, 2 + m, -1]/(Gamma[2 + m] Gamma[ -2 m + n])).
FORMULA
t(n,m)=(Gamma[1 - m + n] Hypergeometric2F1Regularized[1, 1 + 2 m - n, 2 + m, -1])/Gamma[ -2 m + n].
EXAMPLE
{0, 0},
{1, 1},
{0, 3, 3, 0},
{1, 7, 7, 1},
{0, 4, 15, 15, 4, 0},
{1, 11, 31, 31, 11, 1},
{0, 5, 26, 63, 63, 26, 5, 0},
{1, 16, 57, 127, 127, 57, 16, 1},
{0, 6, 42, 120, 255, 255, 120, 42, 6, 0},
{1, 22, 99, 247, 511, 511, 247, 99, 22, 1},
{0, 7, 64, 219, 502, 1023, 1023, 502, 219, 64, 7, 0}
MATHEMATICA
In[97]:= Table[Join[Table[(Gamma[1-m+n] Hypergeometric2F1Regularized[1, 1+2 m-n, 2+m, -1])/Gamma[ -2 m+n], {m, Floor[n/2], 0, -1}], Table[(Gamma[1-m+n] Hypergeometric2F1Regularized[1, 1+2 m-n, 2+m, -1])/Gamma[ -2 m+n], {m, 0, Floor[n/2]}]], {n, 0, 10}]; Flatten[%]
CROSSREFS
KEYWORD
nonn,uned
AUTHOR
Roger L. Bagula and Gary W. Adamson, Sep 14 2008
STATUS
approved