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 A300945 Rectangular array A(n, k) = hypergeom([-k, k + n/2 - 1], [1], -4) with row n >= 0 and k >= 0, read by ascending antidiagonals. 5
 1, 1, 1, 1, 3, 25, 1, 5, 43, 425, 1, 7, 65, 661, 7025, 1, 9, 91, 965, 10515, 116625, 1, 11, 121, 1345, 15105, 171097, 1951625, 1, 13, 155, 1809, 20995, 243525, 2828101, 32903225, 1, 15, 193, 2365, 28401, 337877, 4001345, 47284251, 558265825 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Table of n, a(n) for n=0..44. FORMULA T(n, k) = if k = 0 then 1, otherwise 4^k*Sum_{j=0..n} (5/4)^j * binomial(k, j) * binomial(k - 2 + ((n - k)/2), j - 2 + ((n - k)/2)). - Detlef Meya, May 28 2024 EXAMPLE [0] 1, 1, 25, 425, 7025, 116625, 1951625, 32903225, ... [A299845] [1] 1, 3, 43, 661, 10515, 171097, 2828101, 47284251, ... [A299506] [2] 1, 5, 65, 965, 15105, 243525, 4001345, 66622085, ... [3] 1, 7, 91, 1345, 20995, 337877, 5544709, 92234527, ... [A243946] [4] 1, 9, 121, 1809, 28401, 458649, 7544041, 125700129, ... [A084769] [5] 1, 11, 155, 2365, 37555, 610897, 10098997, 168894355, ... [A243947] [6] 1, 13, 193, 3021, 48705, 800269, 13324417, 224028877, ... MATHEMATICA Arow[n_, len_] := Table[Hypergeometric2F1[-k, k + n/2 - 1, 1, -4], {k, 0, len}]; Table[Print[Arow[n, 7]], {n, 0, 6}]; T[n_, k_] := If[k==0, 1, 4^k*Sum[(5/4)^j*Binomial[k, j]*Binomial[k - 2 + ((n - k)/2), j - 2 + ((n - k)/2)] , {j, 0, n}]]; Flatten[Table[T[n, k], {n, 0, 8}, {k, 0, n}]] (* Detlef Meya, May 28 2024 *) CROSSREFS Cf. A299845, A299506, A243946, A084769, A243947. Cf. A300946. Sequence in context: A297481 A297533 A080202 * A234319 A224873 A085836 Adjacent sequences: A300942 A300943 A300944 * A300946 A300947 A300948 KEYWORD nonn,tabl AUTHOR Peter Luschny, Mar 16 2018 STATUS approved

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Last modified September 15 16:35 EDT 2024. Contains 375938 sequences. (Running on oeis4.)