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A036217
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Expansion of 1/(1-3*x)^5; 5-fold convolution of A000244 (powers of 3).
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16
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1, 15, 135, 945, 5670, 30618, 153090, 721710, 3247695, 14073345, 59108049, 241805655, 967222620, 3794488740, 14635885140, 55616363532, 208561363245, 772903875555, 2833980877035, 10291825290285, 37050571045026
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OFFSET
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0,2
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COMMENTS
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With a different offset, number of n-permutations (n=5) of 4 objects: u, v, z, x with repetition allowed, containing exactly four (4) u's. Example: a(1)=15 because we have uuuuv uuuvu uuvuu uvuuu vuuuu uuuuz uuuzu uuzuu uzuuu zuuuu uuuux uuuxu uuxuu uxuuu xuuuu. - Zerinvary Lajos, Jun 12 2008
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LINKS
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FORMULA
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a(n) = 3^n*binomial(n+4, 4) = 3^n*A000332(n+4).
G.f.: 1/(1-3*x)^5.
E.g.f.: (1/8)*(8 +96*x +216*x^2 +144*x^3 +27*x^4)*exp(3*x). - G. C. Greubel, May 19 2021
Sum_{n>=0} 1/a(n) = 40 - 96*log(3/2).
Sum_{n>=0} (-1)^n/a(n) = 768*log(4/3) - 220. (End)
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MAPLE
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MATHEMATICA
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CoefficientList[Series[1/(1-3x)^5, {x, 0, 30}], x] (* Harvey P. Dale, Jun 13 2017 *)
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PROG
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(Sage) [3^n*binomial(n+4, 4) for n in range(30)] # Zerinvary Lajos, Mar 10 2009
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CROSSREFS
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Sequences of the form 3^n*binomial(n+m, m): A000244 (m=0), A027471 (m=1), A027472 (m=2), A036216 (m=3), this sequence (m=4), A036219 (m=5), A036220 (m=6), A036221 (m=7), A036222 (m=8), A036223 (m=9), A172362 (m=10).
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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