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A118932
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E.g.f.: A(x) = exp( Sum_{n>=0} x^(3^n)/3^((3^n-1)/2) ).
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4
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1, 1, 1, 3, 9, 21, 81, 351, 1233, 10249, 75841, 388411, 3733401, 33702813, 215375889, 1984583511, 19181083041, 141963117201, 1797976123393, 22534941675379, 202605151063081, 2992764505338021, 43182110678814801, 445326641624332623
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OFFSET
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0,4
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COMMENTS
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Equals invariant column vector V that satisfies matrix product A118931*V = V, where A118931(n,k) = n!/[k!(n-3k)!*3^k] for n>=3*k>=0; thus a(n) = Sum_{k=0..[n/3]} A118931(n,k)*a(k), with a(0)=1.
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LINKS
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Table of n, a(n) for n=0..23.
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FORMULA
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a(n) = Sum_{k=0..[n/3]} n!/[k!*(n-3*k)!*3^k] * a(k), with a(0)=1.
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EXAMPLE
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E.g.f. A(x) = exp( x + x^3/3 + x^9/3^4 + x^27/3^13 + x^81/3^40 +...)
= 1 + 1*x + 1*x^2/2! + 3*x^3/3! + 9*x^4/4! + 21*x^5/5!+ 81*x^6/6!+...
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PROG
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(PARI) {a(n)=if(n==0, 1, sum(k=0, n\3, n!/(k!*(n-3*k)!*3^k)*a(k)))} (PARI) /* Defined by E.G.F.: */ {a(n)=n!*polcoeff( exp(sum(k=0, ceil(log(n+1)/log(3)), x^(3^k)/3^((3^k-1)/2))+x*O(x^n)), n, x)}
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CROSSREFS
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Cf. A118931; variants: A118930, A118935.
Sequence in context: A073947 A062811 A001470 * A053499 A218003 A146909
Adjacent sequences: A118929 A118930 A118931 * A118933 A118934 A118935
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, May 06 2006
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STATUS
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approved
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