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Search: id:A122993
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| A122993 |
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G.f.: A(x) = Product_{n>=0} 1/( 1 - x/(1-x)^n )^( 1/2^(n+1) ). |
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+0
2
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| 1, 1, 2, 5, 14, 43, 145, 538, 2194, 9796, 47635, 250811, 1421509, 8623112, 55693506, 381175374, 2753122695, 20909082797, 166448275680, 1385010594903, 12016912542681, 108481226052096, 1016937780320981, 9882191461530141
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Apparently, also the number of permutations in S_n avoiding {bar 1}43{bar 5}2 (i.e. every occurrence of 432 is contained in an occurrence of a 14352). - Lara Pudwell (lpudwell(AT)math.rutgers.edu), Apr 25 2008
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EXAMPLE
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A(x) = (1-x)^(-1/2) * (1 - x/(1-x))^(-1/4) * (1 - x/(1-x)^2)^(-1/8) * (1 - x/(1-x)^3)^(-1/16) * ...
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PROGRAM
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(PARI) {a(n)=round(polcoeff(prod(i=0, 6*n+10, 1/(1-x/(1-x)^i +x*O(x^n))^(1/2^(i+1))), n))}
(PARI) {a(n)=local(A); if(n<0, 0, A=1+O(x); for(k=1, n, A=truncate(A)+x*O(x^k); A+=substvec(A, [x, y], [x/(1-x*y+O(x^k)), y*(1-x*y)]) -A^2*(1-x)); subst(polcoeff(A, n), y, 1))} /* Michael Somos Oct 21 2006 */
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CROSSREFS
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Cf. A122992.
Adjacent sequences: A122990 A122991 A122992 this_sequence A122994 A122995 A122996
Sequence in context: A137550 A047970 A137551 this_sequence A137552 A137553 A137554
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Sep 23 2006
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