A226932 Numerators in expansion of 1/(1-log(1+x)).

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

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: A156295 A350216 A362309 * A245167 A070414 A195870

Adjacent sequences: A226929 A226930 A226931 * A226933 A226934 A226935

Keyword

sign,frac

Author

N. J. A. Sloane, Jul 31 2013

Status

approved