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Search: id:A073384
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| A073384 |
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Seventh convolution of A000129(n+1) (generalized (2,1)-Fibonacci, called Pell numbers), n>=0, with itself. |
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+0
2
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| 1, 16, 152, 1104, 6756, 36624, 181224, 834768, 3628746, 15035504, 59829704, 229977904, 857894388, 3117321456, 11067753144, 38492230704, 131417200419, 441252045408, 1459330704656, 4760342849504
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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a(n)=sum(b(k)*c(n-k), k=0..n) with b(k) := A000129(k+1) and c(k) := A073383(k).
a(n)=sum((2^n)*binomial(n-k+7, 7)*binomial(n-k, k)*(1/4)^k, k=0..floor(n/2)).
a(n)= ((34083315+46659654*n+24858030*n^2+6632968*n^3+939632*n^4+67304*n^5+1912*n^6)*(n+1)*U(n+1)+(7204365+13225068*n+8230910*n^2+2411744*n^3+362968*n^4+27088*n^5+792*n^6)*(n+2)*U(n))/(2^18*3^2*5*7), with U(n) := A000129(n+1), n>=0.
G.f.: 1/(1-(2+x)*x)^8.
a(n)=F'''''''(n+8, 2)/7!, that is, 1/7! times the 7th derivative of the (n+8)th Fibonacci polynomial evaluated at x=2. - T. D. Noe (noe(AT)sspectra.com), Jan 19 2006
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CROSSREFS
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Eighth (m=7) column of triangle A054456, A073383.
Sequence in context: A006420 A049351 A023014 this_sequence A022644 A076071 A096136
Adjacent sequences: A073381 A073382 A073383 this_sequence A073385 A073386 A073387
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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), Aug 2, 2002
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