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A036220
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Expansion of 1/(1-3*x)^7; 7-fold convolution of A000244 (powers of 3).
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14
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1, 21, 252, 2268, 17010, 112266, 673596, 3752892, 19702683, 98513415, 472864392, 2192371272, 9865670724, 43257171636, 185387878440, 778629089448, 3211844993973, 13036312034361, 52145248137444, 205836505805700, 802762372642230, 3096369151620030
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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+6, 6).
G.f.: 1/(1-3*x)^7.
E.g.f.: (1/80)*(80 + 1440*x + 5400*x^2 + 7200*x^3 + 4050*x^4 + 972*x^5 + 81*x^6)*exp(3*x). - G. C. Greubel, May 19 2021
Sum_{n>=0} 1/a(n) = 1173/5 - 576*log(3/2).
Sum_{n>=0} (-1)^n/a(n) = 18432*log(4/3) - 26508/5. (End)
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MAPLE
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MATHEMATICA
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Table[3^n*Binomial[n+6, 6], {n, 0, 30}] (* G. C. Greubel, May 19 2021 *)
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PROG
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(Sage) [3^n*binomial(n+6, 6) 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), A036219 (m=5), this sequence (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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