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Search: id:A137359
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| A137359 |
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Sum_{k <= n/2 } k*binomial(n-2k, 3k). |
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+0
2
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| 0, 0, 0, 0, 0, 1, 4, 10, 20, 35, 58, 98, 176, 333, 640, 1213, 2242, 4052, 7226, 12835, 22842, 40788, 72952, 130344, 232200, 412190, 729466, 1288216, 2272012, 4003795, 7050358, 12404345, 21801674, 38275760, 67125420, 117604174, 205865368, 360090917, 629414866
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OFFSET
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0,7
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REFERENCES
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D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.4.
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FORMULA
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G.f.: x^5*(1-x)^2/(x^5+x^3-3*x^2+3*x-1)^2. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 23 2008]
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MAPLE
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a:= n-> (Matrix([[10, 4, 1, 0$7]]). Matrix (10, (i, j)-> if i=j-1 then 1 elif j=1 then [6, -15, 20, -15, 8, -7, 6, -2, 0, -1][i] else 0 fi)^n)[1, 8]: seq (a(n), n=0..50); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 23 2008]
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CROSSREFS
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Cf. A137356-A137361, A136444.
Adjacent sequences: A137356 A137357 A137358 this_sequence A137360 A137361 A137362
Sequence in context: A057319 A034223 A139748 this_sequence A134987 A058539 A008112
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KEYWORD
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nonn
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AUTHOR
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D. E. Knuth, Apr 11 2008
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