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

Author

Stefano Spezia, Jul 08 2021

Keywords

• nonn
• easy

Links

• 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).

Crossrefs

Cf. A000079, A007531, A128789, A257872 (-8*log(2)), A317614.

Programs

Mathematica

LinearRecurrence[{8,-24,32,-16},{0,1,6,30,120,420},30]

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...