login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A009269 Expansion of e.g.f. exp(tanh(x)*log(1+x)). 1
1, 0, 2, -3, 12, -70, 370, -2436, 20048, -175176, 1679368, -18271000, 216489416, -2751576048, 37874200208, -560956931640, 8845252164864, -148215651070272, 2635014886145472, -49474969983055872, 977864639612813440 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

a(n) = Sum_{m=1..n} Sum_{i=0..n-2*m} Stirling1(i+m,m)*binomial(n,i+m)* Sum_{k=0..n-i-2*m} binomial(k+m-1,m-1)*(k+m)!*(-1)^(2*m+k)*2^(n-k-i-2*m)*Stirling2(n-i-m,k+m), n > 0, a(0)=1. - Vladimir Kruchinin, Jun 01 2011

a(n) ~ n! * (-1)^n * n^(tanh(1)-1) / GAMMA(tanh(1)). - Vaclav Kotesovec, Jan 24 2015

MATHEMATICA

With[{nn=20}, CoefficientList[Series[Exp[Tanh[x]Log[1+x]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jan 19 2014 *)

CoefficientList[Series[(1 + x)^Tanh[x], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 24 2015 *)

PROG

(Maxima)

a(n):=sum(sum((stirling1(i+m, m)*binomial(n, i+m)*sum(binomial(k+m-1, m-1)*(k+m)!*(-1)^(2*m+k)*2^(n-k-i-2*m)*stirling2(n-i-m, k+m), k, 0, n-i-2*m)), i, 0, n-2*m), m, 1, n); /* Vladimir Kruchinin, Jun 01 2011 */

CROSSREFS

Sequence in context: A012911 A264726 A099805 * A012396 A013012 A009594

Adjacent sequences:  A009266 A009267 A009268 * A009270 A009271 A009272

KEYWORD

sign,easy

AUTHOR

R. H. Hardin

EXTENSIONS

Extended with signs by Olivier Gérard, Mar 15 1997

Previous Mathematica program replaced by Harvey P. Dale, Jan 19 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 20 01:38 EDT 2019. Contains 325168 sequences. (Running on oeis4.)