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 A244492 Triangle read by rows: T(n,k) (n>=2, 0 <= k <= n-2) = n!/(2^i*i!*k!), where k=n-2i (or 0 for entries with wrong parity). 0
 1, 0, 3, 3, 0, 6, 0, 15, 0, 10, 15, 0, 45, 0, 15, 0, 105, 0, 105, 0, 21, 105, 0, 420, 0, 210, 0, 28, 0, 945, 0, 1260, 0, 378, 0, 36, 945, 0, 4725, 0, 3150, 0, 630, 0, 45 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..44. J. East and R. D. Gray, Idempotent generators in finite partition monoids and related semigroups, arXiv preprint arXiv:1404.2359 [math.GR], 2014-2016. EXAMPLE Triangle begins: 1; 0, 3; 3, 0, 6; 0, 15, 0, 10; 15, 0, 45, 0, 15; 0, 105, 0, 105, 0, 21; 105, 0, 420, 0, 210, 0, 28; 0, 945, 0, 1260, 0, 378, 0, 36; 945, 0, 4725, 0, 3150, 0, 630, 0, 45; ... MATHEMATICA T[n_, k_] := With[{i = (n-k)/2}, If[EvenQ[n-k], n!/(2^i i! k!), 0]]; Table[T[n, k], {n, 2, 10}, {k, 0, n-2}] // Flatten (* Jean-François Alcover, Nov 25 2018 *) CROSSREFS This is A099174 without the two rightmost diagonals. Sequence in context: A193451 A335809 A322215 * A210838 A319256 A354618 Adjacent sequences: A244489 A244490 A244491 * A244493 A244494 A244495 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, Jul 05 2014 STATUS approved

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Last modified June 8 00:26 EDT 2023. Contains 363157 sequences. (Running on oeis4.)