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A226932 Numerators in expansion of 1/(1-log(1+x)). 1
1, 1, 1, 1, 1, 7, 19, 3, 5, 13, 199, 1663, -10819, 117119, -3676549, 10412641, -1060597, 726672017, -981455179, 102949234721, -1838522272459, 372770223277, -18951133622563, 415806440998633, -3750247247013611, 141278065655009, -1221840877070910001, 15727225740325641197 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

REFERENCES

M. Kauers and P. Paule, The Concrete Tetrahedron, Springer 2011, p. 22.

LINKS

Table of n, a(n) for n=0..27.

FORMULA

a(n) = numerator(Sum_{k=0..n}(k!*Stirling1(n,k))/n!). - Vladimir Kruchinin, Oct 10 2016

EXAMPLE

1+x+(1/2)*x^2+(1/3)*x^3+(1/6)*x^4+(7/60)*x^5+(19/360)*x^6+(3/70)*x^7+(5/336)*x^8+(13/756)*x^9+...

MATHEMATICA

Table[Numerator@ Sum[(k! StirlingS1[n, k])/n!, {k, 0, n}], {n, 0, 27}] (* Michael De Vlieger, Oct 08 2016 *)

PROG

(PARI) x = 'x + O('x^30); apply(x->numerator(x), Vec(1/(1-log(1+x)))) \\ Michel Marcus, Oct 08 2016

(Sage)

def A226932_list(dim):

    C = [[0 for k in range(m+1)] for m in range(dim)]

    C[0][0] = 1; F = [1]

    for m in (1..dim-1):

        F.append(F[m-1]*m)

        C[m][m] = -C[m-1][m-1]

        for k in range(m-1, 0, -1):

            S = sum(C[m][k+i-1]/F[i] for i in (2..m-k+1))

            C[m][k] = -(C[m-1][k-1] + S)

    return [(-1)^j*sum(r).numerator() for j, r in enumerate(C)]

print A226932_list(28) # Peter Luschny, Sep 15 2017

CROSSREFS

Cf. A226933.

Sequence in context: A219290 A156238 A156295 * A245167 A070414 A195870

Adjacent sequences:  A226929 A226930 A226931 * A226933 A226934 A226935

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Jul 31 2013

STATUS

approved

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Last modified November 17 00:08 EST 2019. Contains 329209 sequences. (Running on oeis4.)