A346174 Inverse binomial transform of A317614.

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

Offset

0,3

Links

Table of n, a(n) for n=0..29.

N. J. A. Sloane, Transforms

Eric Weisstein's World of Mathematics, Binomial Transform

Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16).

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

Adjacent sequences: A346171 A346172 A346173 * A346175 A346176 A346177

Keyword

nonn,easy

Author

Stefano Spezia, Jul 08 2021

Status

approved