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A137636
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a(n) = Sum_{k=0..n} C(2k+1,k)*C(2k+1,n-k) ; equals row 1 of square array A137634; also equals the convolution of A137635 and A073157.
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4
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1, 4, 19, 94, 474, 2431, 12609, 65972, 347524, 1840680, 9792986, 52296799, 280163091, 1504969409, 8103433329, 43722788132, 236340999038, 1279602656590, 6938126362948, 37668424608552, 204751452911832, 1114151447523038
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| G.f.: A(x) = R(x)*G(x), where R(x) = 1/sqrt(1-4x(1+x)^2) is the g.f. of A137635 and G(x) = (1-sqrt(1-4x(1+x)^2))/(2x(1+x)) is the g.f. of A073157.
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PROG
| (PARI) {a(n)=sum(k=0, n, binomial(2*k+1, k)*binomial(2*k+1, n-k))} /* Using the g.f.: */ {a(n)=local(R=1/sqrt(1-4*x*(1+x +x*O(x^n))^2), G=(1-sqrt(1-4*x*(1+x)^2+x^2*O(x^n)))/(2*x*(1+x+x*O(x^n)))); polcoeff(R*G, n, x)}
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CROSSREFS
| Cf. A137634, A137635, A137637, A137638, A073157.
Sequence in context: A122369 A005978 A083065 * A027618 A020060 A122394
Adjacent sequences: A137633 A137634 A137635 * A137637 A137638 A137639
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jan 31 2008
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