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A346174 Inverse binomial transform of A317614. 0
0, 1, 6, 30, 120, 420, 1344, 4032, 11520, 31680, 84480, 219648, 559104, 1397760, 3440640, 8355840, 20054016, 47628288, 112066560, 261488640, 605552640, 1392771072, 3183476736, 7235174400, 16357785600, 36805017600, 82443239424, 183911841792, 408692981760, 904963031040 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Binomial Transform
FORMULA
O.g.f.: x*(1 - 2*x + 6*x^2 - 8*x^3 + 4*x^4)/(1 - 2*x)^4.
E.g.f.: x*(1 + exp(2*x)*(3 + 6*x + 2*x^2))/4.
a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4) for n > 5.
a(n) = 2^(n-4)*n*(n + 1)*(n + 2) with a(0) = 0 and a(1) = 1.
a(n) = A000079(n-4)*A007531(n+2) for n > 1.
a(n) ~ A128789(n)/16.
Sum_{n>0} 1/a(n) = 8*log(2) - 13/3 = 1.21184411114622914200452363833...
MATHEMATICA
LinearRecurrence[{8, -24, 32, -16}, {0, 1, 6, 30, 120, 420}, 30]
CROSSREFS
Cf. A000079, A007531, A128789, A257872 (-8*log(2)), A317614.
Sequence in context: A319889 A319870 A055281 * A182349 A371036 A215225
KEYWORD
nonn,easy
AUTHOR
Stefano Spezia, Jul 08 2021
STATUS
approved

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Last modified March 29 11:45 EDT 2024. Contains 371278 sequences. (Running on oeis4.)