A191817 E.g.f. sin(arctan(log(1+x))).

0, 1, -1, -1, 12, -36, -120, 2148, -9744, -64572, 1454220, -8208828, -96161472, 2479373064, -15862726152, -295638678072, 8425875692160, -56585105164080, -1653901130160720, 50485379331780720, -336548011774484160, -14999134695936065280, 482781746150042834880, -2963015696186375016960

Offset

0,5

Links

Table of n, a(n) for n=0..23.

Formula

a(n) = sum(k=0..(n-1)/2, binomial(2*k,k)*2^(-2*k)*(-1)^(k)*(2*k+1)!*stirling1(n,2*k+1)), n>0.

Mathematica

Table[Sum[Binomial[2 k, k] 2^(-2 k) (-1)^k * (2 k + 1)! * StirlingS1[n, 2 k + 1], {k, 0, (n - 1)/2}], {n, 0, 23}] (* Michael De Vlieger, Jul 13 2015 *)

Prog

(Maxima)
a(n):=sum(binomial(2*k, k)*2^(-2*k)*(-1)^(k)*(2*k+1)!*stirling1(n, 2*k+1), k, 0, (n-1)/2);
(PARI) x='x+O('x^33); concat([0], Vec(serlaplace(sin(atan(log(1+x)))))) \\ Joerg Arndt, Jul 13 2015

Crossrefs

Sequence in context: A055551 A355386 A073403 * A270840 A064518 A238923

Adjacent sequences: A191814 A191815 A191816 * A191818 A191819 A191820

Keyword

sign

Author

Vladimir Kruchinin, Jun 17 2011

Extensions

Terms corrected by Anders Claesson, Jul 13 2015

Status

approved