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Search: id:A132306
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| A132306 |
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a(n) = Sum_{k=0..2n-1} C(2n-1,k)*trinomial(n,k) for n>0 with a(0)=1. |
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1
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| 1, 2, 18, 179, 1874, 20202, 221943, 2470827, 27777618, 314642708, 3585365618, 41054041602, 471980219543, 5444542749674, 62987391100239, 730515277512729, 8490829425196626, 98878672140171984, 1153433769999190212
(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_{k=0..2n} C(2n,k)*trinomial(n,k)/2 for n>0 with a(0)=1 ; also, a(n) = Sum_{k=0..2n} C(-2n-1,k)*trinomial(n,k)/2 for n>0 with a(0)=1 ; also, a(n) = Sum_{k=0..2n} C(-2n,k)*trinomial(n,k) ; where trinomial(n,k) = [x^k] (1 + x + x^2)^n.
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PROGRAM
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(PARI) {a(n)=sum(k=0, 2*n, binomial(2*n-1, k)*polcoeff((1+x+x^2)^n, k))} (PARI) {a(n)=if(n==0, 1, sum(k=0, 2*n, binomial(2*n, k)*polcoeff((1+x+x^2)^n, k))/2)} (PARI) {a(n)=if(n==0, 1, sum(k=0, 2*n, binomial(-2*n-1, k)*polcoeff((1+x+x^2)^n, k))/2)} (PARI) {a(n)=sum(k=0, 2*n, binomial(-2*n, k)*polcoeff((1+x+x^2)^n, k))}
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CROSSREFS
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Cf. A082759.
Sequence in context: A052665 A092473 A073558 this_sequence A099044 A161122 A019581
Adjacent sequences: A132303 A132304 A132305 this_sequence A132307 A132308 A132309
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Aug 18 2007
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