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A073389
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Second convolution of A002605(n) (generalized (2,2)-Fibonacci), n>=0, with itself.
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5
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1, 6, 30, 128, 504, 1872, 6672, 23040, 77616, 256288, 832416, 2666496, 8441600, 26454528, 82174464, 253280256, 775316736, 2358812160, 7137023488, 21487386624, 64401106944, 192229535744, 571630694400
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n)=sum(b(k)*c(n-k), k=0..n) with b(k) := A002605(k) and c(k) := A073388(k).
a(n)=(2^n)*sum(binomial(n-k+2, 2)*binomial(n-k, k)*(1/2)^k, k=0..floor(n/2)).
a(n)=(3+n)*((n+1)*U(n+1)+(n+2)*U(n))/12, with U(n) := A002605(n), n>=0.
G.f.: 1/(1-2*x*(1+x))^3.
G.f.:sage: taylor( mul(x/(1 - 2*x - 2*x^2) for i in xrange(1,4)),x,0,25)# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 03 2009]
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EXAMPLE
| sage: taylor( mul(x/(1 - 2*x - 2*x^2) for i in xrange(1,4)),x,0,25)#solution >> x^3 + 6*x^4 + 30*x^5 + 128*x^6 + 504*x^7 + 1872*x^8 + 6672*x^9 + 23040*x^10 +.....+ 7137023488*x^21 + 21487386624*x^22 + 64401106944*x^23 + 192229535744*x^24 + 571630694400*x^25 + etc... [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 03 2009]
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MATHEMATICA
| CoefficientList[Series[1/(1-2x(1+x))^3, {x, 0, 25}], x] (* From Harvey P. Dale, Mar 14 2011 *)
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CROSSREFS
| Third (m=2) column of triangle A073387, A073388.
Sequence in context: A131458 A032205 A007465 * A036068 A162743 A081895
Adjacent sequences: A073386 A073387 A073388 * A073390 A073391 A073392
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Aug 2, 2002
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