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A299338
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Expansion of 1 / ((1 - x)^7*(1 + x)^6).
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4
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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
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OFFSET
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0,3
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COMMENTS
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Same as A000579 but with repeated terms.
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LINKS
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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).
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FORMULA
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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.
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MATHEMATICA
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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 *)
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PROG
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(PARI) Vec(1 / ((1 - x)^7*(1 + x)^6) + O(x^40))
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CROSSREFS
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Cf. A000579, A001769, A060099, A299335, A299336, A299337.
Sequence in context: A111217 A339339 A198341 * A341246 A246039 A186142
Adjacent sequences: A299335 A299336 A299337 * A299339 A299340 A299341
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KEYWORD
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nonn,easy
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AUTHOR
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Colin Barker, Feb 07 2018
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STATUS
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approved
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