A009329 E.g.f. log(1+sin(tan(x))).

0, 1, -1, 3, -10, 41, -232, 1299, -10064, 74609, -720384, 6787811, -78009600, 898506649, -11977120768, 163241051315, -2480763381760, 39007280136801, -666957211828224, 11866656488375747, -225809770695098368

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

a(n) = 4*sum(k=0..(n-1)/2, ((-1)^(n-k+1)*sum(r=0..k, ((sum(i=0..(n-2*k)/2, (2*i-n+2*k)^(2*r+n-2*k)*(-1)^i*binomial(n-2*k,i)))*sum(j=2*r+n-2*k..n, binomial(j-1,2*r+n-2*k-1)*j!*2^(n-j-1)*(-1)^(j)*stirling2(n,j)))/(2*r+n-2*k)!))/((n-2*k)*2^(n-2*k))). - Vladimir Kruchinin, Jun 11 2011

a(n) ~ 2 * (-1)^(n+1) * (n-1)! / arctan(Pi/2)^n. - Vaclav Kotesovec, Jun 26 2014

Mathematica

CoefficientList[Series[Log[1+Sin[Tan[x]]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jun 26 2014 *)

Prog

(Maxima)
a(n):=4*sum(((-1)^(n-k+1)*sum(((sum((2*i-n+2*k)^(2*r+n-2*k)*(-1)^i*binomial(n-2*k, i), i, 0, (n-2*k)/2))*sum(binomial(j-1, 2*r+n-2*k-1)*j!*2^(n-j-1)*(-1)^(j)*stirling2(n, j), j, 2*r+n-2*k, n))/(2*r+n-2*k)!, r, 0, k))/((n-2*k)*2^(n-2*k)), k, 0, (n-1)/2); /* Vladimir Kruchinin, Jun 11 2011*/

Crossrefs

Bisections are A012016 and A012240.

Sequence in context: A084786 A156170 A245502 * A009364 A308951 A295236

Adjacent sequences: A009326 A009327 A009328 * A009330 A009331 A009332

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved