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Search: id:A137638
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| 1, 3, 15, 72, 361, 1840, 9505, 49578, 260540, 1377328, 7316373, 39020372, 208809544, 1120621368, 6029023185, 32507001876, 175604614108, 950233307930, 5149691511432, 27946158749572, 151843410356906, 825949622559366
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OFFSET
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0,2
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FORMULA
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G.f.: A(x) = 2*(1+x)/((1+2*x + G(x))*G(x)) where G(x) = sqrt(1 - 4*x*(1+x)^2). a(n) = Sum_{k=0..n} Sum_{j=0..k} C(n-k+2*j,j)*C(n-k+2*j,k-j).
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PROGRAM
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(PARI) {a(n)=sum(k=0, n, sum(j=0, k, binomial(2*j+n-k, j)*binomial(2*j+n-k, k-j)))} /* Using the g.f.: */ {a(n)=local(G=sqrt(1 - 4*x*(1+x)^2 +x*O(x^n))); polcoeff(2*(1+x)/((1+2*x+G)*G), n)}
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CROSSREFS
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Cf. A137634, A137635, A137636, A137637.
Sequence in context: A033876 A009174 A123942 this_sequence A055837 A124543 A007142
Adjacent sequences: A137635 A137636 A137637 this_sequence A137639 A137640 A137641
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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), Jan 31 2008
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