A088022 - OEIS

A088022

a(n) = floor(sum_{k>=0} k^n /(k!)^3); related to generalized Bell numbers.

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

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OFFSET

0,1

LINKS

Table of n, a(n) for n=0..28.

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