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A134531
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G.f.: Sum_{n>=0} a(n)*x^n/[n!*2^(n*(n-1)/2)] = log( Sum_{n>=0} x^n/[n!*2^(n*(n-1)/2)] ).
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3
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0, 1, -1, 5, -79, 3377, -362431, 93473345, -56272471039, 77442176448257, -239804482525402111, 1650172344732021412865, -24981899010711376986398719, 825164608171793476724052668417, -59053816996641612758331731690504191, 9102696765174239045811746247171452452865
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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FORMULA
| Equals column 0 of triangle A134530, which is the matrix log of triangle A111636, where A111636(n,k) = (2^k)^(n-k)*C(n,k).
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EXAMPLE
| Let g.f. G(x) = Sum_{n>=0} a(n)*x^n/[ n! * 2^(n*(n-1)/2) ]
then exp(G(x)) = Sum_{n>=0} x^n/[ n! * 2^(n*(n-1)/2) ];
G.f.: G(x) = x - x^2/4 + 5x^3/48 - 79x^4/1536 + 3377x^5/122880 +...
exp(G(x)) = 1 + x + x^2/4 + x^3/48 + x^4/1536 + x^5/122880 +...
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PROG
| (PARI) {a(n)=n!*2^(n*(n-1)/2)*polcoeff(log(sum(k=0, n, x^k/(k!*2^(k*(k-1)/2)))+x*O(x^n)), n)}
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CROSSREFS
| Cf. related triangles: A134530, A111636; A118197 (variant); A011266.
Sequence in context: A197232 A152297 A141828 * A062250 A131284 A105917
Adjacent sequences: A134528 A134529 A134530 * A134532 A134533 A134534
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KEYWORD
| sign
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Oct 30 2007
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