A299338 Expansion of 1 / ((1 - x)^7*(1 + x)^6).

1, 1, 7, 7, 28, 28, 84, 84, 210, 210, 462, 462, 924, 924, 1716, 1716, 3003, 3003, 5005, 5005, 8008, 8008, 12376, 12376, 18564, 18564, 27132, 27132, 38760, 38760, 54264, 54264, 74613, 74613, 100947, 100947, 134596, 134596, 177100, 177100, 230230, 230230

Offset: 0

Author

Colin Barker, Feb 07 2018

Keywords

• nonn
• easy

Comments

Same as A000579 but with repeated terms.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,6,-6,-15,15,20,-20,-15,15,6,-6,-1,1).

Crossrefs

Cf. A000579, A001769, A060099, A299335, A299336, A299337.

Programs

Mathematica

CoefficientList[Series[1/((1-x)^7(1+x)^6),{x,0,50}],x] (* or *) LinearRecurrence[ {1,6,-6,-15,15,20,-20,-15,15,6,-6,-1,1},{1,1,7,7,28,28,84,84,210,210,462,462,924},50] (* Harvey P. Dale, Oct 09 2018 *)

PARI

Vec(1 / ((1 - x)^7*(1 + x)^6) + O(x^40))

Formula

a(n) = (2*n^6 + 84*n^5 + 1400*n^4 + 11760*n^3 + 51968*n^2 + 112896*n + 92160) / 92160 for n even.

a(n) = (2*n^6 + 72*n^5 + 1010*n^4 + 6960*n^3 + 24278*n^2 + 39048*n + 20790) / 92160 for n odd.

a(n) = a(n-1) + 6*a(n-2) - 6*a(n-3) - 15*a(n-4) + 15*a(n-5) + 20*a(n-6) - 20*a(n-7) - 15*a(n-8) + 15*a(n-9) + 6*a(n-10) - 6*a(n-11) - a(n-12) + a(n-13) for n>12.