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Search: id:A056567
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| A056567 |
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Fibonomial coefficients. |
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+0
2
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| 1, 55, 4895, 352440, 27372840, 2063912136, 157373300370, 11948265189630, 908637119420910, 69056421075989160, 5249543573067466872, 399024295188779925720, 30331388438447118520355
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OFFSET
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0,2
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FORMULA
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a(n)= A010048(n+9, 9)=: Fibonomial(n+9, 9).
G.f. 1/p(10, n) with p(10, n)= 1-55*x-1870*x^2+19635*x^3+85085*x^4 -136136*x^5-85085*x^6+19635*x^7+1870*x^8-55*x^9-x^10 = (1-x-x^2)*(1+4*x-x^2)*(1-11*x-x^2)*(1+29*x-x^2)*(1-76*x-x^2) (n=10 row polynomial of signed Fibonomial triangle A055870; see this entry for Knuth and Riordan references.).
Recursion: a(n)=76*a(n-1)+a(n-2)+((-1)^n)*A056565(n), n >= 2, a(0)=1, a(1)=55.
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MAPLE
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with(combinat):a:=n->1/2227680*fibonacci(n)*fibonacci(n+1)*fibonacci(n+2)*fibonacci(n+3)*fibonacci(n+4)*fibonacci(n+5)*fibonacci(n+6)*fibonacci(n+7)*fibonacci(n+8): seq(a(n), n=1..13); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 07 2007
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CROSSREFS
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Cf. A010048, A000045, A001654-8, A056565-6, A001076 (signed), A049666, A049667 (signed), A049669.
Sequence in context: A060077 A035323 A103918 this_sequence A119081 A119051 A119083
Adjacent sequences: A056564 A056565 A056566 this_sequence A056568 A056569 A056570
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jul 10 2000
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