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Search: id:A118930
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| A118930 |
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E.g.f.: A(x) = exp( Sum_{n>=0} x^(2^n)/2^(2^n-1) ). |
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4
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| 1, 1, 2, 4, 13, 41, 166, 652, 3494, 18118, 114076, 681176, 5016892, 35377564, 288204008, 2232198256, 21124254181, 191779964597, 2011347229114, 19840403629108, 231266808172181, 2553719667653281, 31743603728993542
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Equals invariant column vector V that satisfies matrix product A100861*V = V, where Bessel numbers A100861(n,k) = n!/[k!(n-2k)!*2^k] give the number of k-matchings of the complete graph K(n).
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FORMULA
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a(n) = Sum_{k=0..[n/2]} n!/[k!*(n-2*k)!*2^k] * a(k), with a(0)=1. a(n) = Sum_{k=0..[n/2]} A100861(n,k)*a(k), with a(0)=1.
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EXAMPLE
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E.g.f. A(x) = exp( x + x^2/2 + x^4/2^3 + x^8/2^7 + x^16/2^15 +...)
= 1 + 1*x + 2*x^2/2! + 4*x^3/3! + 13*x^4/4! + 41*x^5/5!+ 166*x^6/6!+...
Using coefficients A100861(n,k) = n!/[k!(n-2k)!*2^k]:
a(5) = 1*a(0) +10*a(1) +15*a(2) = 1*1 +10*1 +15*2 = 41.
a(6) = 1*a(0) +15*a(1) +45*a(2) +15*a(3) = 1*1 +15*1 +45*2 +15*4 = 166.
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PROGRAM
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(PARI) {a(n)=if(n==0, 1, sum(k=0, n\2, n!/(k!*(n-2*k)!*2^k)*a(k)))} (PARI) /* Defined by E.G.F.: */ {a(n)=n!*polcoeff( exp(sum(k=0, #binary(n), x^(2^k)/2^(2^k-1))+x*O(x^n)), n, x)}
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CROSSREFS
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Cf. A100861; variants: A118932, A118935.
Sequence in context: A133453 A085422 A065601 this_sequence A087214 A002771 A050624
Adjacent sequences: A118927 A118928 A118929 this_sequence A118931 A118932 A118933
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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), May 06 2006
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