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 A350464 Table read by rows. Interpolating the swinging factorial (A056040) and the double factorial (A001147). 2
 1, 0, 1, 0, 1, 3, 0, 2, 15, 15, 0, 6, 91, 210, 105, 0, 6, 690, 2835, 3150, 945, 0, 30, 5214, 42405, 79695, 51975, 10395, 0, 20, 44772, 666666, 2057055, 2207205, 945945, 135135, 0, 140, 384756, 11274900, 54879825, 90090000, 62432370, 18918900, 2027025 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Table of n, a(n) for n=0..44. FORMULA The partial Bell polynomials Y_{2*n, k}(Z) applied to the list Z of the aerated swinging factorials (A056040). EXAMPLE Triangle starts: [0] 1; [1] 0, 1; [2] 0, 1, 3; [3] 0, 2, 15, 15; [4] 0, 6, 91, 210, 105; [5] 0, 6, 690, 2835, 3150, 945; [6] 0, 30, 5214, 42405, 79695, 51975, 10395; [7] 0, 20, 44772, 666666, 2057055, 2207205, 945945, 135135; MATHEMATICA Swing[n_] := n! / Floor[n/2]!^2; Z[n_] := Flatten[Table[{0, Swing[j]}, {j, 0, n}]]; T[n_, k_] := BellY[2 n, k, Z[n - k]]; Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten CROSSREFS Cf. A350465 (row sums), A350466 (alternating row sums). Cf. A056040, A001147, A001880. Sequence in context: A302381 A303102 A302953 * A247706 A361527 A247704 Adjacent sequences: A350461 A350462 A350463 * A350465 A350466 A350467 KEYWORD nonn,tabl AUTHOR Peter Luschny, Mar 13 2022 STATUS approved

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Last modified April 14 15:45 EDT 2024. Contains 371665 sequences. (Running on oeis4.)