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A121725
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Generalized central coefficients for k=3.
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4
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1, 1, 10, 19, 190, 442, 4420, 11395, 113950, 312814, 3128140, 8960878, 89608780, 264735892, 2647358920, 8006545891, 80065458910, 246643289830, 2466432898300, 7711583225338, 77115832253380
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Hankel transform of a(n) is 9^binomial(n+1,2). Case k=3 of T(n,k)=2*k^2*(2k)^n*INT(x^n*sqrt(1-x^2)/(1+k^2-2kx),x,-1,1)/pi. T(n,k) has Hankel transform (k^2)^binomial(n+1,2). k=1 corresponds to C(n,floor(n/2)).
Expansion of c(9x^2)/(1-xc(9x^2)), where c(x) is the g.f. of A000108 . Reversion of x(1+x)/(1+2x+10x^2). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 09 2007
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FORMULA
| a(n)=18*6^n*INT(x^n*sqrt(1-x^2)/(10-6x),x,-1,1)/pi
a(n) = Sum_{k, 0<=k<=floor(n/2)} A009766(n-k,k)*3^2k . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 18 2006
a(n)=Sum_{k, 0<=k<=n}A120730(n,k)*9^(n-k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 09 2007
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CROSSREFS
| Sequence in context: A177167 A073222 A110463 * A110368 A006050 A045646
Adjacent sequences: A121722 A121723 A121724 * A121726 A121727 A121728
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Aug 17 2006
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