A007311 Reversion of o.g.f. for Bell numbers (A000110) omitting a(0)=1.

1, -2, 3, -5, 7, -14, 11, -66, -127, -992, -5029, -30899, -193321, -1285300, -8942561, -65113125, -494605857, -3911658640, -32145949441, -274036507173, -2419502677445, -22093077575496, -208364964369913, -2027216779571754, -20323053380033763, -209715614081160850

Offset: 1

Author

N. J. A. Sloane, Mira Bernstein

Keywords

• sign

Comments

As the definition says, this entry deliberately omits the zero-th term 1. - N. J. A. Sloane, Jun 16 2021

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Index entries for reversions of series

Crossrefs

Cf. A000110.

Programs

Maple

read transforms; A := series(exp(exp(x)-1),x,60); SERIESTOLISTMULT(%); subsop(1=NULL,%); REVERT(%);
# Alternative, using function CompInv from A357588:
CompInv(26, n -> combinat:-bell(n)); # Peter Luschny, Oct 05 2022

PARI

a(n)=if(n<1,0,polcoeff(serreverse(-1+serlaplace(exp(exp(x+x*O(x^n))-1))),n))

Formula

G.f. A(x) satisfies: A(x) = x - Sum_{k>=2} Bell(k) * A(x)^k. - Ilya Gutkovskiy, Apr 22 2020

Extensions

Signs corrected Dec 24 2001