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 A338654 T(n, k) = 2^n * Product_{j=1..k}((j/2)^((-1)^(j - 1)). Triangle read by rows, for 0 <= k <= n. 2
 1, 2, 1, 4, 2, 2, 8, 4, 4, 6, 16, 8, 8, 12, 6, 32, 16, 16, 24, 12, 30, 64, 32, 32, 48, 24, 60, 20, 128, 64, 64, 96, 48, 120, 40, 140, 256, 128, 128, 192, 96, 240, 80, 280, 70, 512, 256, 256, 384, 192, 480, 160, 560, 140, 630, 1024, 512, 512, 768, 384, 960, 320, 1120, 280, 1260, 252 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Felix Fröhlich, Table of n, a(n) for n = 0..10000 EXAMPLE Triangle start:                              [0] 1                            [1] 2, 1                           [2] 4, 2, 2                         [3] 8, 4, 4, 6                       [4] 16, 8, 8, 12, 6                   [5] 32, 16, 16, 24, 12, 30                 [6] 64, 32, 32, 48, 24, 60, 20              [7] 128, 64, 64, 96, 48, 120, 40, 140          [8] 256, 128, 128, 192, 96, 240, 80, 280, 70      [9] 512, 256, 256, 384, 192, 480, 160, 560, 140, 630 MAPLE T := (n, k) -> 2^n*mul((j/2)^((-1)^(j - 1)), j = 1 .. k): seq(seq(T(n, k), k=0..n), n=0..9); # Recurrence: Trow := proc(n) if n = 0 then return [1] fi; Trow(n - 1); n^irem(n, 2) * (4/n)^irem(n + 1, 2) * %[n]; [op(2 * %%), %] end: seq(print(Trow(n)), n = 0..9); PROG (PARI) t(n, k) = 2^n * prod(j=1, k, ((j/2)^((-1)^(j - 1)))) trianglerows(n) = for(x=0, n-1, for(y=0, x, print1(t(x, y), ", ")); print("")) /* Print upper 10 rows of the triangle as follows: */ trianglerows(10) \\ Felix Fröhlich, Apr 22 2021 CROSSREFS T(n, 0) = A000079(n), T(n, n) = A056040(n), T(2*n, n) = A253665(n). Cf. A328002 (row sums), A163590. Sequence in context: A104733 A201703 A153281 * A130584 A339046 A265911 Adjacent sequences:  A338651 A338652 A338653 * A338655 A338656 A338657 KEYWORD nonn,tabl AUTHOR Peter Luschny, Apr 22 2021 STATUS approved

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Last modified July 24 11:17 EDT 2021. Contains 346273 sequences. (Running on oeis4.)