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 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 (list; graph; refs; listen; history; text; internal format)
 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 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 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

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Last modified January 23 16:47 EST 2020. Contains 331172 sequences. (Running on oeis4.)