A188489 - OEIS

%I #15 Apr 01 2018 06:26:05

%S 1,1,2,8,61,797,16021,457285,17529203,867230231,53745914922,

%T 4076301322848,371301496685164,39992538951200636,5027440719872343598,

%U 729432303460596468394,120977789712983152108734,22743262423568258626295550

%N Exponential transform of (A000275 number of pairs of permutations with rise/rise forbidden).

%H Vaclav Kotesovec, <a href="/A188489/b188489.txt">Table of n, a(n) for n = 0..250</a>

%F G.f.: A(x) = exp( Sum_{n>=1} A000275(n)*x^n/n ) where A000275 is the number of pairs of permutations with rise/rise forbidden.

%F a(n) ~ c * n! * (n-1)! / r^n, where r = 1/4*BesselJZero[0,1]^2 = 1.44579649073669613 and c = 1/(sqrt(r) * BesselJ(1, 2*sqrt(r))) = 1.6019746969280466266484... - _Vaclav Kotesovec_, Mar 02 2014, updated Apr 01 2018

%e G.f.: A(x) = 1 + x + 2*x^2 + 8*x^3 + 61*x^4 + 797*x^5 + 16021*x^6 +...

%e log(A(x)) = x + 3*x^2/2 + 19*x^3/3 + 211*x^4/4 + 3651*x^5/5 + 90921*x^6/6 +...+ A000275(n)*x^n/n +...

%o (PARI) {A000275(n)=n!^2*4^n*polcoeff(1/besselj(0, x+x*O(x^(2*n))), 2*n)}

%o {a(n)=polcoeff(exp(sum(m=1,n,A000275(m)*x^m/m)+x*O(x^n)),n)}

%Y Cf. A000275 (log), A115368.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Apr 01 2011