A188489 Exponential transform of (A000275 number of pairs of permutations with rise/rise forbidden).

1, 1, 2, 8, 61, 797, 16021, 457285, 17529203, 867230231, 53745914922, 4076301322848, 371301496685164, 39992538951200636, 5027440719872343598, 729432303460596468394, 120977789712983152108734, 22743262423568258626295550

Offset: 0

Author

Paul D. Hanna, Apr 01 2011

Keywords

• nonn

Examples

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

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..250

Crossrefs

Cf. A000275 (log), A115368.

Programs

PARI

{A000275(n)=n!^2*4^n*polcoeff(1/besselj(0, x+x*O(x^(2*n))), 2*n)}
{a(n)=polcoeff(exp(sum(m=1,n,A000275(m)*x^m/m)+x*O(x^n)),n)}

Formula

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.

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