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A007311 Reversion of o.g.f. for Bell numbers (A000110) omitting a(0)=1.
(Formerly M0676)
2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
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
FORMULA
G.f. A(x) satisfies: A(x) = x - Sum_{k>=2} Bell(k) * A(x)^k. - Ilya Gutkovskiy, Apr 22 2020
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
PROG
(PARI) a(n)=if(n<1, 0, polcoeff(serreverse(-1+serlaplace(exp(exp(x+x*O(x^n))-1))), n))
CROSSREFS
Cf. A000110.
Sequence in context: A309249 A294727 A348352 * A031345 A206702 A279953
KEYWORD
sign
AUTHOR
EXTENSIONS
Signs corrected Dec 24 2001
STATUS
approved

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)