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A136637
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a(n) = Sum_{k=0..n} C(n, k) * C(2^k*3^(n-k), n).
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3
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1, 5, 72, 6089, 3326498, 12405917044, 336474648380394, 69883583587428350874, 115099747754889610404191160, 1536533057081060754026861201898620, 168527150638482484315370462123098294514192
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OFFSET
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0,2
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COMMENTS
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Equals row sums of triangle A136635.
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LINKS
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Table of n, a(n) for n=0..10.
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FORMULA
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G.f.: A(x) = Sum_{n>=0} log(1 + (2^n + 3^n)*x )^n / n!.
a(n) ~ 3^(n^2) / n!. - Vaclav Kotesovec, Jul 02 2016
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EXAMPLE
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More generally,
if Sum_{n>=0} log(1 + (p^n + r*q^n)*x )^n / n! = Sum_{n>=0} b(n)*x^n,
then b(n) = Sum_{k=0..n} C(n,k)*r^(n-k) * C(p^k*q^(n-k), n)
(a result due to Vladeta Jovovic, Jan 13 2008).
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MATHEMATICA
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Table[Sum[Binomial[n, k]*Binomial[2^k*3^(n-k), n], {k, 0, n}], {n, 0, 15}] (* Vaclav Kotesovec, Jul 02 2016 *)
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PROG
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(PARI) {a(n)=sum(k=0, n, binomial(n, k)*binomial(2^k*3^(n-k), n))}
(PARI) /* Using g.f.: */ {a(n)=polcoeff(sum(i=0, n, log(1+(2^i+3^i)*x)^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), A136638 (antidiagonal sums).
Sequence in context: A197324 A197977 A307932 * A319767 A138623 A206280
Adjacent sequences: A136634 A136635 A136636 * A136638 A136639 A136640
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic and Paul D. Hanna, Jan 15 2008
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STATUS
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approved
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