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 A331327 T(n, k) = [x^k] Pochhammer(x, n-k) for n >= 0, 0 <= k <= floor(n/2). Irregular triangle read by rows. 0
 1, 0, 0, 1, 0, 1, 0, 2, 1, 0, 6, 3, 0, 24, 11, 1, 0, 120, 50, 6, 0, 720, 274, 35, 1, 0, 5040, 1764, 225, 10, 0, 40320, 13068, 1624, 85, 1, 0, 362880, 109584, 13132, 735, 15, 0, 3628800, 1026576, 118124, 6769, 175, 1, 0, 39916800, 10628640, 1172700, 67284, 1960, 21 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 LINKS FORMULA Rows are the antidigonals of A132393. EXAMPLE Triangle starts: [ 0] 1; [ 1] 0; [ 2] 0, 1; [ 3] 0, 1; [ 4] 0, 2,     1; [ 5] 0, 6,     3; [ 6] 0, 24,    11,    1; [ 7] 0, 120,   50,    6; [ 8] 0, 720,   274,   35,   1; [ 9] 0, 5040,  1764,  225,  10; [10] 0, 40320, 13068, 1624, 85, 1; MAPLE A331327row := n -> seq(coeff(expand(pochhammer(x, n-k)), x, k), k=0..n/2): seq(A331327row(n), n=0..13); MATHEMATICA T[n_, k_] := Abs[StirlingS1[n - k, k]]; Table[T[n, k], {n, 0, 13}, {k, 0, Floor[n/2]}] // Flatten CROSSREFS Row sums are: 1, 0, A237653. Cf. A132393. Sequence in context: A122930 A066387 A180663 * A301924 A262071 A011312 Adjacent sequences:  A331324 A331325 A331326 * A331328 A331329 A331330 KEYWORD nonn,tabf AUTHOR Peter Luschny, Jan 25 2020 STATUS approved

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Last modified March 28 17:51 EDT 2020. Contains 333103 sequences. (Running on oeis4.)