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 A354977 Triangle read by rows. T(n, k) = Sum_{j=0..n}((-1)^(n-j)*binomial(n, j)*j^(n+k)) / n!. 2
 1, 1, 1, 1, 3, 7, 1, 6, 25, 90, 1, 10, 65, 350, 1701, 1, 15, 140, 1050, 6951, 42525, 1, 21, 266, 2646, 22827, 179487, 1323652, 1, 28, 462, 5880, 63987, 627396, 5715424, 49329280, 1, 36, 750, 11880, 159027, 1899612, 20912320, 216627840, 2141764053 (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) = Stirling2(n + k, n). EXAMPLE Triangle T(n, k) begins: [0] 1; [1] 1, 1; [2] 1, 3, 7; [3] 1, 6, 25, 90; [4] 1, 10, 65, 350, 1701; [5] 1, 15, 140, 1050, 6951, 42525; [6] 1, 21, 266, 2646, 22827, 179487, 1323652; [7] 1, 28, 462, 5880, 63987, 627396, 5715424, 49329280; [8] 1, 36, 750, 11880, 159027, 1899612, 20912320, 216627840, 2141764053; MAPLE T := (n, k) -> add((-1)^(n - j)*binomial(n, j)*j^(n + k), j = 0..n) / n!: seq(seq(T(n, k), k = 0..n), n = 0..8); CROSSREFS T(n,1) = A000217, T(n,n) = A007820, A354978 (row sums), A048993. Sequence in context: A010781 A019806 A199589 * A080172 A133065 A335815 Adjacent sequences: A354974 A354975 A354976 * A354978 A354979 A354980 KEYWORD nonn,tabl AUTHOR Peter Luschny, Jun 15 2022 STATUS approved

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Last modified September 10 16:10 EDT 2024. Contains 375790 sequences. (Running on oeis4.)