

A141947


A manufactured symmetrical triangular sequence of coefficients based on: t(n,m)=(Gamma[1  m + n] Hypergeometric2F1Regularized[1, 1 + 2 m  n, 2 + m, 1])/Gamma[ 2 m + n]. The function is taken have backward and half forward.


0



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
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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])).


LINKS

Table of n, a(n) for n=1..72.


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[1m+n] Hypergeometric2F1Regularized[1, 1+2 mn, 2+m, 1])/Gamma[ 2 m+n], {m, Floor[n/2], 0, 1}], Table[(Gamma[1m+n] Hypergeometric2F1Regularized[1, 1+2 mn, 2+m, 1])/Gamma[ 2 m+n], {m, 0, Floor[n/2]}]], {n, 0, 10}]; Flatten[%]


CROSSREFS

Cf. A052509.
Sequence in context: A104548 A085707 A320253 * A216804 A010607 A325018
Adjacent sequences: A141944 A141945 A141946 * A141948 A141949 A141950


KEYWORD

nonn,uned


AUTHOR

Roger L. Bagula and Gary W. Adamson, Sep 14 2008


STATUS

approved



