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A116363
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a(n) = dot product of row n in Catalan triangle A033184 with row n in Pascal's triangle.
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1
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1, 2, 7, 30, 141, 698, 3571, 18686, 99385, 535122, 2908863, 15932766, 87809541, 486421770, 2706138987, 15110359038, 84637982961, 475381503266, 2676447372535, 15100548901790, 85357620588541, 483304834607322
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n) = Sum_{k=0..n} C(n,k)*C(2*n-k+1,n-k)*(k+1)/(2*n-k+1). G.f. satisfies: d/dx[log(1-4*x*A(x))] = -4*(1-5*x)/(1-13*x+43*x^2-7*x^3).
o.g.f.: 2*(R+x)/(R*(R+x+1)), where R = sqrt(x^2+6*x+1). [From Dan Drake (ddrake(AT)member.ams.org), May 19 2010]
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EXAMPLE
| The dot product of Catalan row 4 and Pascal row 4 equals
a(4) = [14,14,9,4,1]*[1,4,6,4,1] = 141
which is equivalent to obtaining the final term
in these repeated partial sums of Pascal row 4:
1,4, 6, 4, 1
.5,11,15,16
..16,31,47
...47,94
....141
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PROG
| (PARI) a(n)=sum(k=0, n, binomial(n, k)*binomial(2*n-k+1, n-k)*(k+1)/(2*n-k+1))
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CROSSREFS
| Cf. A033184.
Sequence in context: A074416 A097924 A027136 * A186858 A174796 A046648
Adjacent sequences: A116360 A116361 A116362 * A116364 A116365 A116366
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Feb 04 2006
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