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A118589
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E.g.f.: A(x) = exp(x + x^2 + x^3).
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2
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1, 1, 3, 13, 49, 261, 1531, 9073, 63393, 465769, 3566611, 29998101, 262167313, 2394499693, 23249961099, 233439305401, 2439472944961, 26649502709073, 300078056044963, 3498896317045789, 42244252226263281, 524289088799352661
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Equals row sums of triangle A118588.
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FORMULA
| a(n)=n!*sum(sum(binomial(j,n-3*k+2*j)*binomial(k,j),j,0,k)/k!,k,1,n), n>0. [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Sep 01 2010]
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MATHEMATICA
| Range[0, 21]!*CoefficientList[ Series[ Exp[x*(1-x^3)/(1 - x)], {x, 0, 21}], x] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 23 2007
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PROG
| (PARI) {a(n)=n!*polcoeff(exp(x+x^2+x^3 +x*O(x^n)), n, x)}
(Other) a(n):=n!*sum(sum(binomial(j, n-3*k+2*j)*binomial(k, j), j, 0, k)/k!, k, 1, n); (for Maxima) [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Sep 01 2010]
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CROSSREFS
| Cf. A118588 (triangle), A119013 (eigenvector).
Sequence in context: A094978 A178934 A045908 * A113237 A196907 A116427
Adjacent sequences: A118586 A118587 A118588 * A118590 A118591 A118592
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), May 08 2006
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