A187111 Series inversion of A007296.

1, 2, -1, 3, -11, 44, -187, 827, -3751, 17313, -81004, 383390, -1833029, 8843224, -43007753, 210670655, -1038597645, 5149654796, -25664518105, 128493771585, -645988558986, 3259776393676, -16505191207192, 83828620957326, -426961815072785

Offset: 0

Author

Vladimir Kruchinin, Mar 05 2011

Keywords

• sign
• less

Comments

The generating function A007296(x) = x - 2*x^2 + 5*x^3 - 15*x^4 + ... is a reversion of A008578(x) = x + 2*x^2 + 3*x^3 + ... with A007296(A008578(x))=x. The ordinary generating function A(x) = x/(x - 2*x + 5*x^2 - 15*x^3 + ...) = 1 + 2*x - x^2 + ... of this sequence here obeys A008578(x)=x*A(A008578(x)).

Programs

Maple

read("transforms") ;
Lp := [ 0,1,seq(ithprime(i),i=1..25) ] ;
a007296 := REVERT(Lp) ;
a007296x := add( op(i,a007296)*x^i,i=1..nops(a007296)) ;
a187111x := taylor(x/a007296x ,x=0,nops(a007296)+1);
for n from 0 to nops(a007296)-1 do printf("%d,",coeftayl(a187111x,x=0,n)) ; end do; # R. J. Mathar, Mar 29 2011