A112498 Third column of second-order Eulerian triangle A008517 divided by 2.

3, 29, 164, 726, 2805, 9975, 33630, 109424, 347519, 1085313, 3349848, 10253994, 31203945, 94561643, 285716018, 861472836, 2593592883, 7800176565, 23441423340, 70410252350, 211411111133, 634610819679, 1904620987014

Offset: 3

Author

Wolfdieter Lang, Oct 14 2005

Keywords

• nonn
• easy

Comments

See A004301 for the doubled sequence.

Links

• Index entries for linear recurrences with constant coefficients, signature (10,-40,82,-91,52,-12).

Crossrefs

Cf. A000295 (one half of second column).

Formula

a(n)=A008517(n, 3)/2.

G.f.: x^3*(3-x-6*x^2)/(((1-x)^3)*((1-2*x)^2)*(1-3*x)). See the comment on column g.f.s under A008517.

a(n) = 3*a(n-1) + (2*n-3)*(2^(n-1)-n), n>3, with a(3)=3.

a(n)= 3*A112502(n-3) - A112502(n-4) - 6*A112502(n-5), n>=5.