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 A088022 a(n) = floor(sum_{k>=0} k^n /(k!)^3); related to generalized Bell numbers. 1
 2, 1, 1, 2, 3, 6, 12, 28, 68, 176, 484, 1409, 4334, 14002, 47357, 167157, 614297, 2345730, 9290084, 38092233, 161436136, 706061825, 3182452003, 14764717643, 70429572474, 345075959701, 1734987079149, 8943648710357, 47228775626154 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS FORMULA B(n) := sum_{k>=0} k^n/(k!)^3 = A000996(n)*B(0) + A000997(n)*B(1) + A000998(n)*B(2) where B(0)=2.129702548983..., B(1)=1.264181150389..., B(2)=1.542838638501...; observe that these shift 3 places left under binomial transform: A000996={1, 0, 0, 1, 1, 1, 2, 6, 17, 44, 112, 304, 918, ...}, A000997={0, 1, 0, 0, 1, 2, 3, 5, 12, 36, 110, 326, 963, ...}, A000998={0, 0, 1, 0, 0, 1, 3, 6, 11, 24, 69, 227, 753, ...}; here A000998 is offset with 5 leading terms: {0, 0, 1, 0, 0}. EXAMPLE a(8) = 68 = floor(17*2.1297 + 12*1.2641 + 11*1.5428) = floor(68.3463). CROSSREFS Cf. A086880, A000996, A000997, A000998. Sequence in context: A025259 A212359 A130030 * A284999 A016732 A077948 Adjacent sequences: A088019 A088020 A088021 * A088023 A088024 A088025 KEYWORD nonn AUTHOR Paul D. Hanna, Sep 19 2003 STATUS approved

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Last modified March 20 18:36 EDT 2023. Contains 361391 sequences. (Running on oeis4.)