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Search: id:A136638
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| A136638 |
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a(n) = Sum_{k=0..[n/2]} C(n-k, k) * C(3^(n-2*k)*2^k, n-k). |
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+0
4
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| 1, 3, 38, 2955, 1666194, 6775599252, 204212962736426, 47025953519744215608, 84798028785462127288681736, 1219731316443261012339196962784452, 141916030637329352970764084182705691263552
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OFFSET
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0,2
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COMMENT
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Equals antidiagonal sums of triangle A136635.
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FORMULA
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G.f.: A(x) = Sum_{n>=0} log(1 + 3^n*x + 2^n*x^2)^n / n!.
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EXAMPLE
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More generally, if Sum_{n>=0} log(1 + b*p^n*x + d*q^n*x^2)^n/n! = Sum_{n>=0} a(n)*x^n then a(n) = Sum_{k=0..[n/2]} C(n-k,k)*b^(n-2k)*d^k*C(p^(n-2k)*q^k,n-k).
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PROGRAM
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(PARI) {a(n)=sum(k=0, n\2, binomial(n-k, k)*binomial(3^(n-2*k)*2^k, n-k))} (PARI) /* Using g.f.: */ {a(n)=polcoeff(sum(i=0, n, log(1+3^i*x+2^i*x^2)^i/i!), n, x)}
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CROSSREFS
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Cf. A136635 (triangle), A014070 (main diagonal), A136393 (column 0), A136636 (column 1), A136637 (row sums).
Sequence in context: A109518 A062155 A099022 this_sequence A134106 A082954 A050392
Adjacent sequences: A136635 A136636 A136637 this_sequence A136639 A136640 A136641
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu) and Paul D. Hanna (pauldhanna(AT)juno.com), Jan 15 2008
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