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A036219
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Expansion of 1/(1-3*x)^6; 6-fold convolution of A000244 (powers of 3).
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14
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1, 18, 189, 1512, 10206, 61236, 336798, 1732104, 8444007, 39405366, 177324147, 773778096, 3288556908, 13660159464, 55616363532, 222465454128, 875957725629, 3400777052442, 13036312034361, 49400761393368, 185252855225130, 688082033693340, 2533392942234570
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = 3^n*binomial(n+5, 5).
G.f.: 1/(1-3*x)^6.
E.g.f.: (1/40)*(40 + 600*x + 1800*x^2 + 1800*x^3 + 675*x^4 + 81*x^5)*exp(3*x). - G. C. Greubel, May 19 2021
Sum_{n>=0} 1/a(n) = 240*log(3/2) - 385/4.
Sum_{n>=0} (-1)^n/a(n) = 3840*log(4/3) - 4415/4. (End)
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MAPLE
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MATHEMATICA
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Table[3^n*Binomial[n+5, 5], {n, 0, 30}] (* G. C. Greubel, May 19 2021 *)
CoefficientList[Series[1/(1-3x)^6, {x, 0, 30}], x] (* or *) LinearRecurrence[ {18, -135, 540, -1215, 1458, -729}, {1, 18, 189, 1512, 10206, 61236}, 30] (* Harvey P. Dale, Jan 02 2022 *)
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PROG
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(Sage) [3^n*binomial(n+5, 5) 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), A036217 (m=4), this sequence (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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