A180614 - OEIS

%I #5 Jun 20 2016 22:48:36

%S 1,-1,5,-60,1284,-41520,1818480,-99906240,6615483840,-547250618880,

%T 64405640678400,-10795621264243200,1874134190688883200,

%U -168421749610341427200,-33755136201402065049600,-12663782909587871373312000,33228107527756336198907904000,-9780793395112024278861643776000,-17994218650633803932152655560704000,15220589020710912054512237626933248000,19029826524235967059926689085261791232000

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

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

%F 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.

%e 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!) -+...

%o (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])}

%o for(n=1, 30, print1(a(n), ", "))

%Y Cf. A180610.

%K eigen,sign

%O 1,3

%A _Paul D. Hanna_, Sep 12 2010