A180614 G.f. satisfies: L(x) = L(x*exp(x))/(1+x) = Sum_{n>=1} a(n)*x^n/(n!*(n-1)!).

1, -1, 5, -60, 1284, -41520, 1818480, -99906240, 6615483840, -547250618880, 64405640678400, -10795621264243200, 1874134190688883200, -168421749610341427200, -33755136201402065049600, -12663782909587871373312000, 33228107527756336198907904000, -9780793395112024278861643776000, -17994218650633803932152655560704000, 15220589020710912054512237626933248000, 19029826524235967059926689085261791232000

Offset: 1

Author

Paul D. Hanna, Sep 12 2010

Keywords

• eigen
• sign

Comments

G.f. L(x) forms the column g.f.s in the matrix log of the Riordan array (exp(x), x*exp(x)).

Examples

			G.f.: L(x) = x - 1*x^2/(2!*1!) + 5*x^3/(3!*2!) - 60*x^4/(4!*3!) + 1284*x^5/(5!*4!) - 41520*x^6/(6!*5!) + 1818480*x^7/(7!*6!) -+...
		

Crossrefs

Cf. A180610.

Programs

PARI

{a(n)=local(M=matrix(n+1,n+1,r,c,if(r>=c,polcoeff(exp(c*x+x*O(x^n)),r-c))),L=sum(n=1,#M,-(M^0-M)^n/n));if(n<1,0,n!*(n-1)!*L[n+1,1])}
for(n=1, 30, print1(a(n), ", "))

Formula

a(n) = A180610(n)/n for n>0; the g.f. for this sequence is the same as for A180610; see A180610 for more formulas and examples.