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 A244430 E.g.f.: exp( Sum_{n>=1} Fibonacci(n)*x^n/n ). 7
 1, 1, 2, 8, 44, 316, 2776, 28912, 347888, 4750064, 72548576, 1225540096, 22686824512, 456700011328, 9932944782464, 232113573798656, 5799735585095936, 154302762658308352, 4354977806995644928, 129961223706359609344, 4088626884119702752256, 135246429574930409348096 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..410 Tomislav Doslic and R. Sharafdini, Hosoya Index of Splices, Bridges, and Necklaces, in Distance, Symmetry, and Topology in Carbon Nanomaterials, 2016, pp 147-156. Part of the Carbon Materials: Chemistry and Physics book series (CMCP, volume 9), doi:10.1007/978-3-319-31584-3_10. See page 9, at the end of section 2, where a sequence with this recurrence although with different initial conditions is mentioned. FORMULA E.g.f.: ( (1 + x/Phi) / (1 - Phi*x) )^(sqrt(5)/5) where Phi = (sqrt(5)+1)/2. E.g.f.: exp( Integral 1/(1-x-x^2) dx ). a(n) ~ n! * 5^(1/(2*sqrt(5))) * n^(1/sqrt(5)-1) * ((1+sqrt(5))/2)^(n-1/sqrt(5)) / GAMMA(1/sqrt(5)). - Vaclav Kotesovec, Jun 28 2014 a(n) = (n-1)*a(n-1) + (n-2)*(n-3)*a(n-2) for a(0)=0, a(1)=a(2)=1. - G. C. Greubel, May 02 2015 E.g.f.: sqrt(5)*Phi^(-2/sqrt(5))*( B((Phi + x)/sqrt(5); 2/(sqrt(5) Phi), (2 Phi)/sqrt(5)) - B(Phi/sqrt(5); 2/(sqrt(5) Phi), (2 Phi)/sqrt(5)) ), where B(z; a, b) is the Incomplete Beta function and a(0)=0, a(1)=a(2)=1. - G. C. Greubel, May 02 2015 EXAMPLE E.g.f.: A(x) = 1 + x + 2*x^2/2! + 8*x^3/3! + 44*x^4/4! + 316*x^5/5! + 2776*x^6/6! +... where log(A(x)) = x + x^2/2 + 2*x^3/3 + 3*x^4/4 + 5*x^5/5 + 8*x^6/6 + 13*x^7/7 + 21*x^8/8 + 34*x^9/9 +...+ A000045(n)*x^n/n +... MAPLE f:= gfun:-rectoproc({a(n) = n*a(n-1) + (n-1)*(n-2)*a(n-2), a(0)=1, a(1)=1}, a(n), remember): seq(f(n), n=0..50); # Robert Israel, May 22 2015 MATHEMATICA a[ n_ ] := a[n] =(n-2)*(n-3)a[n-2]+(n-1)*a[n-1]; a[0] := 0; a[1] := 1 (* G. C. Greubel, May 02 2015 *) RecurrenceTable[{a[0]==0, a[1]==1, a[n]==(n-2)*(n-3)a[n-2]+(n-1)*a[n-1]}, a, {n, 20}] (* G. C. Greubel, May 02 2015 *) PROG (PARI) {a(n)=n!*polcoeff(exp(intformal(1/(1-x-x^2 +x*O(x^n)))), n)} for(n=0, 30, print1(a(n), ", ")) (MAGMA) [n le 2 select 1 else (n-1)*Self(n-1)+(n^2-5*n+6)*Self(n-2): n in [1..30]]; // Vincenzo Librandi, May 03 2015 CROSSREFS Cf. A244451, A244432, A000045. Sequence in context: A216234 A123307 A293905 * A190818 A253949 A126101 Adjacent sequences:  A244427 A244428 A244429 * A244431 A244432 A244433 KEYWORD nonn AUTHOR Paul D. Hanna, Jun 27 2014 STATUS approved

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Last modified May 19 16:36 EDT 2019. Contains 323395 sequences. (Running on oeis4.)