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Search: id:A036217
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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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+0
2
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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
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n)=A027465(n+5,5) (O. Gerard's triangle).
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 (zerinvarylajos(AT)yahoo.com), Jun 12 2008
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FORMULA
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a(n) = 3^n*binomial(n+4, 4); G.f. 1/(1-3*x)^5.
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MAPLE
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seq(binomial(n+4, 4)*3^n, n=0..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 12 2008
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PROGRAM
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(Other) SAGE: [lucas_number2(n, 3, 0)*binomial(n, 4)/81 for n in xrange(4, 25)] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 10 2009]
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CROSSREFS
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A000244, A027465.
Sequence in context: A027630 A027629 A023013 this_sequence A022643 A125378 A155648
Adjacent sequences: A036214 A036215 A036216 this_sequence A036218 A036219 A036220
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KEYWORD
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easy,nonn
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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