A392547 Expansion of 1 / ((1-x)^6 - x^7).

1, 6, 21, 56, 126, 252, 462, 793, 1299, 2080, 3367, 5733, 10556, 20944, 43453, 91104, 188480, 380190, 745066, 1420916, 2650221, 4869285, 8888489, 16261025, 30031820, 56231526, 106791426, 205108561, 396480142, 767426451, 1481274767, 2843775112, 5424947523

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,-15,20,-15,6,-1,1).

Formula

a(n) = Sum_{k=0..floor(n/7)} binomial(n-k+5,n-7*k).

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) + a(n-7).

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(1/((1-x)^6-x^7))

Crossrefs

Cf. A005709, A049017, A392543, A392544, A392545, A392546.

Sequence in context: A090581 A000389 A143980 * A140228 A264926 A006090

Adjacent sequences: A392544 A392545 A392546 * A392548 A392549 A392550

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 15 2026

Status

approved