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

0,3

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).

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.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A111217 A339339 A198341 * A341246 A246039 A186142

Adjacent sequences: A299335 A299336 A299337 * A299339 A299340 A299341

Keyword

nonn,easy

Author

Colin Barker, Feb 07 2018

Status

approved