0,2

a(n)= A010048(n+10, 10)=: Fibonomial(n+10, 10).

G.f. 1/p(11, n) with p(11, n)= 1-89*x-4895*x^2+83215*x^3+582505*x^4 -1514513*x^5-1514513*x^6+582505*x^7+83215*x^8-4895*x^9-89*x^10+x^11 = (1+x)*(1-3*x+x^2)*(1+7*x+x^2)*(1-18*x+x^2)*(1+47*x+x^2)*(1-123*x+x^2) (n=8 row polynomial of signed Fibonomial triangle A055870; see this entry for Knuth and Riordan references.)

Recursion: a(n)=123*a(n-1)-a(n-2)+((-1)^n)*A056566(n), n >= 2, a(0)=1, a(1)=89.

with(combinat):a:=n->1/122522400*fibonacci(n)*fibonacci(n+1)*fibonacci(n+2)*fibo\ nacci(n+3)*fibonacci(n+4)*fibonacci(n+5)*fibonacci(n+6)*fibonacci(n+7)*fibonacci\ (n+8)*fibonacci(n+9): seq(a(n), n=1..12); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 07 2007

a := n-> (Matrix(11, (i, j)-> if (i=j-1) then 1 elif j=1 then [1514513, -582505, -83215, 4895, 89, -1][abs(i-11/2)+1/2] else 0 fi)^n)[1, 1]; seq (a(n), n=0..11); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 15 2008]

Cf. A010048, A000045, A001654-8, A056565-7, A001906, A004187 (signed), A049660, A049668 (signed), A049670.

Sequence in context: A093948 A116254 A086695 this_sequence A167398 A023330 A059766

Adjacent sequences: A056565 A056566 A056567 this_sequence A056569 A056570 A056571

nonn,easy

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jul 10 2000