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A036222
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Expansion of 1/(1-3*x)^9; 9-fold convolution of A000244 (powers of 3).
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3
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1, 27, 405, 4455, 40095, 312741, 2189187, 14073345, 84440070, 478493730, 2583866142, 13389124554, 66945622770, 324428787270, 1529449997130, 7035469986798, 31659614940591, 139674771796725, 605257344452475
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n)=A027465(n+9,9) (O. Gerard's triangle).
With a different offset, number of n-permutations (n>=8) of 4 objects: u, v, z, x with repetition allowed, containing exactly eight (8) u's. Example: a(1)=27 because we have uuuuuuuuv, uuuuuuuuz, uuuuuuuux, uuuuuuuvu, uuuuuuuzu, uuuuuuuxu, uuuuuuvuu, uuuuuuzuu, uuuuuuxuu, uuuuuvuuu, uuuuuzuuu, uuuuuxuuu, uuuuvuuuu, uuuuzuuuu, uuuuxuuuu, uuuvuuuuu, uuuzuuuuu, uuuxuuuuu, uuvuuuuuu, uuzuuuuuu, uuxuuuuuu, uvuuuuuuu, uzuuuuuuu, uxuuuuuuu, vuuuuuuuu, zuuuuuuuu, xuuuuuuuu. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 23 2008
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..400
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FORMULA
| a(n) = 3^n*binomial(n+8, 8); G.f. 1/(1-3*x)^9.
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MAPLE
| seq(binomial(n+8, 8)*3^n, n=0..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 23 2008
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MATHEMATICA
| Table[Binomial[n + 8, 8]*3^n, {n, 0, 20}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 31 2010]
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PROG
| (Other) SAGE:[lucas_number2(n, 3, 0)*binomial(n, 8)/3^8 for n in xrange(8, 27)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 13 2009]
(MAGMA) [3^n*Binomial(n+8, 8): n in [0..30]]; // Vincenzo Librandi, Oct 15 2011
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CROSSREFS
| A000244, A027465.
Sequence in context: A000535 A033280 A125462 * A022655 A155988 A096950
Adjacent sequences: A036219 A036220 A036221 * A036223 A036224 A036225
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KEYWORD
| easy,nonn
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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