0,5

-a(n+1), n>=0, also numerators from e.g.f. 1/x-1/ln(1+x), with denominators A075178(n). |a(n+1)|, n>=0, numerators from e.g.f. 1/x+1/ln(1-x) with denominators A075178(n). For formula of unsigned a(n) see A075178.

The signed rationals a(n)/A006233(n) provide the a-sequence for the Stirling2 Sheffer matrix A048993. See the W. Lang link concerning Sheffer a- and z-sequences.

Cauchy numbers of the first type are also called Bernoulli numbers of the second kind.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

A. Adelberg, 2-adic congruences of Norland numbers and of Bernoulli numbers of the second kind, J. Number Theory, 73 (1998), 47-58.

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 294.

H. Jeffreys and B. S. Jeffreys, Methods of Mathematical Physics, Cambridge, 1946, p. 259.

Ming Wu and Hao Pan, Sums of products of Bernoulli numbers of the second kind, Fib. Quart., 45 (2007), 146-150.

T. D. Noe, Table of n, a(n) for n=0..100

W. Lang, Sheffer a- and z-sequences.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Numerator of integral of x(x-1)...(x-n+1) from 0 to 1.

E.g.f.: x/log(1+x).

Numerator of Sum_{k=0..n} A048994(n,k)/(k+1). [From Peter Luschny (peter(AT)luschny.de), Apr 28 2009]

1, 1/2, -1/6, 1/4, -19/30, 9/4, -863/84, 1375/24, -33953/90,...

seq(numer(add(stirling1(n, k)/(k+1), k=0..n)), n=0..20); [From Peter Luschny (peter(AT)luschny.de), Apr 28 2009]

Cf. A006233, A002206, A002207, A002208, A002209, A002657, A002790.

Sequence in context: A040345 A070685 A033339 this_sequence A122549 A039942 A050276

Adjacent sequences: A006229 A006230 A006231 this_sequence A006233 A006234 A006235

sign,frac,nice

N. J. A. Sloane (njas(AT)research.att.com).