A392584 Expansion of 1 / ((1-x)^3 - x^3)^2.

1, 6, 21, 58, 144, 342, 795, 1818, 4095, 9104, 20028, 43692, 94661, 203886, 436905, 932070, 1980648, 4194306, 8854639, 18641346, 39146835, 82021948, 171500436, 357913944, 745654041, 1550960406, 3221225469, 6681060242, 13839339072, 28633115310, 59175104963, 122167958634

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-15,22,-21,12,-4).

Formula

a(n) = Sum_{k=0..floor(n/3)} (k+1) * binomial(n+5,n-3*k).

a(n) = 6*a(n-1) - 15*a(n-2) + 22*a(n-3) - 21*a(n-4) + 12*a(n-5) - 4*a(n-6).

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(1/((1-x)^3-x^3)^2)

Crossrefs

Cf. A024495.

Sequence in context: A381265 A290891 A047520 * A294836 A341221 A143115

Adjacent sequences: A392581 A392582 A392583 * A392585 A392586 A392587

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 17 2026

Status

approved