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Search: id:A073394
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| A073394 |
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Seventh convolution of A002605(n) (generalized (2,2)-Fibonacci), n>=0, with itself. |
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2
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| 1, 16, 160, 1248, 8304, 49344, 269184, 1372800, 6628512, 30584576, 135804416, 583471616, 2436145920, 9919484928, 39503038464, 154230921216, 591550292736, 2232748892160, 8305370185728
(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) := A002605(k) and c(k) := A073393(k).
a(n)=(2^n)*sum(binomial(n-k+7, 7)*binomial(n-k, k)*(1/2)^k, k=0..floor(n/2)).
a(n)= ((2322320+2869040*n+1379232*n^2+332247*n^3+42533*n^4+2757*n^5+71*n^6)*(n+1)*U(n+1)+4*(235900+375554*n+207009*n^2+54174*n^3+7318*n^4+492*n^5+13*n^6)*(n+2)*U(n))/(2^8*3^6*5*7), with U(n) := A002605(n), n>=0.
G.f.: 1/(1-2*x*(1+x))^8.
G.f.: sage: taylor( mul(x/(1 - 2*x - 2*x^2) for i in xrange(1,9)),x,0,26)# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 03 2009]
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EXAMPLE
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sage: taylor( mul(x/(1 - 2*x - 2*x^2) for i in xrange(1,9)),x,0,26)# solution >>x^8 + 16*x^9 + 160*x^10 + 1248*x^11 +.....+ 154230921216*x^23 + 591550292736*x^24 + 2232748892160*x^25 + 8305370185728*x^26 + etc... [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 03 2009]
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CROSSREFS
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Eighth (m=7) column of triangle A073387.
Sequence in context: A041005 A144453 A121036 this_sequence A038846 A079767 A079768
Adjacent sequences: A073391 A073392 A073393 this_sequence A073395 A073396 A073397
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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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