A339029 Expansion of (1 + 4*x - 20*x^2 + 8*x^3 + 33*x^4 - 4*x^5 - 33*x^6)/(1 - 2*x)^4.

1, 12, 52, 168, 497, 1412, 3879, 10360, 27016, 69024, 173264, 428288, 1044480, 2516992, 6001408, 14174208, 33191936, 77127680, 177967104, 408027136, 930021376, 2108424192, 4756275200, 10680270848, 23880794112, 53185871872, 118016180224, 260969594880, 575223627776

Offset: 0

Author

Peter Luschny, Dec 01 2020

Keywords

• nonn

Links

• Paolo Xausa, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16).

Crossrefs

Cf. A339252 (k=2), A339254 (k=3), A333650.

Programs

Maple

gf := (1 + 4*x - 20*x^2 + 8*x^3 + 33*x^4 - 4*x^5 - 33*x^6)/(1 - 2*x)^4:
ser := series(gf, x, 32): seq(coeff(ser, x, n), n = 0..28);

Mathematica

LinearRecurrence[{8, -24, 32, -16}, {1, 12, 52, 168, 497, 1412, 3879}, 30] (* Paolo Xausa, Feb 01 2024 *)

Formula

a(n) = 2^(n-7)*(588 + 367*n + 84*n^2 + 9*n^3) for n >= 3.