A392546 Expansion of 1 / ((1-x)^5 - x^7).

1, 5, 15, 35, 70, 126, 210, 331, 505, 770, 1221, 2080, 3822, 7385, 14501, 28201, 53585, 99043, 178335, 314413, 546806, 946121, 1642244, 2877925, 5107821, 9176831, 16634509, 30281870, 55117511, 99979855, 180425076, 323834920, 578593536, 1030721985, 1834160110, 3265884047

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1,0,1).

Formula

a(n) = Sum_{k=0..floor(n/7)} binomial(n-2*k+4,n-7*k).

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) + a(n-7).

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(1/((1-x)^5-x^7))

Crossrefs

Cf. A005709, A049017, A392543, A392544, A392545, A392547.

Cf. A049016, A079675, A368475, A369803, A369804, A390045.

Sequence in context: A341184 A090580 A000332 * A342213 A390045 A373936

Adjacent sequences: A392543 A392544 A392545 * A392547 A392548 A392549

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 15 2026

Status

approved