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A209923 E.g.f. A(x) satisfies: A( x - x^2/2 - Sum_{n>=3} (n-3)!*x^n/n! ) = x. 1
1, 1, 4, 26, 237, 2778, 39805, 674125, 13174189, 291802238, 7223963796, 197670359937, 5924155984714, 192988681624915, 6789966027406003, 256591956638230811, 10365414610788266136, 445744854494435066418, 20330276980162447348231, 980249560154126513379574 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Compare e.g.f. to the identity: let W(x) = Sum_{n>=1} (n-1)^(n-1)*x^n/n!, then W( x - Sum_{n>=1} x^(n+1)/(n*(n+1)) ) = x.

LINKS

Table of n, a(n) for n=1..20.

EXAMPLE

E.g.f.: A(x) = x + x^2/2! + 4*x^3/3! + 26*x^4/4! + 237*x^5/5! +...

Let R(x) be the series reversion of e.g.f. A(x), then R(x) begins:

R(x) = x - x^2/(1*2) - x^3/(1*2*3) - x^4/(2*3*4) - x^5/(3*4*5) - x^6/(4*5*6) -...

PROG

(PARI) {a(n)=n!*polcoeff(serreverse(x-x^2/2-sum(m=3, n, (m-3)!*x^m/m!) +x*O(x^n)), n)}

for(n=1, 25, print1(a(n), ", "))

CROSSREFS

Sequence in context: A001863 A300698 A244524 * A317339 A304338 A115416

Adjacent sequences:  A209920 A209921 A209922 * A209924 A209925 A209926

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Mar 15 2012

STATUS

approved

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Last modified March 21 20:35 EDT 2019. Contains 321382 sequences. (Running on oeis4.)