A226932 - OEIS

%I #20 Mar 07 2020 12:25:38

%S 1,1,1,1,1,7,19,3,5,13,199,1663,-10819,117119,-3676549,10412641,

%T -1060597,726672017,-981455179,102949234721,-1838522272459,

%U 372770223277,-18951133622563,415806440998633,-3750247247013611,141278065655009,-1221840877070910001,15727225740325641197

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

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

%F a(n) = numerator(Sum_{k=0..n}(k!*Stirling1(n,k))/n!). - _Vladimir Kruchinin_, Oct 10 2016

%e 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+...

%t Table[Numerator@ Sum[(k! StirlingS1[n, k])/n!, {k, 0, n}], {n, 0, 27}] (* _Michael De Vlieger_, Oct 08 2016 *)

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

%o (Sage)

%o def A226932_list(dim):

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

%o     C[0][0] = 1; F = [1]

%o     for m in (1..dim-1):

%o         F.append(F[m-1]*m)

%o         C[m][m] = -C[m-1][m-1]

%o         for k in range(m-1, 0, -1):

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

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

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

%o print(A226932_list(28)) # _Peter Luschny_, Sep 15 2017

%Y Cf. A226933.

%K sign,frac

%O 0,6

%A _N. J. A. Sloane_, Jul 31 2013