The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A086662 Stirling transform of Catalan numbers: Sum_{k=0..n} |Stirling1(n,k)|*C(2*k,k)/(k+1). 2
 1, 1, 3, 13, 72, 481, 3745, 33209, 329868, 3624270, 43608474, 570008803, 8039735704, 121673027607, 1966231022067, 33786076421499, 615043147866660, 11822938288619344, 239298079351004608, 5086498410027323134, 113278368771499790136, 2637549737582063583274, 64082443707327038140602, 1621782672366231029685407 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..200 FORMULA E.g.f.: hypergeom([1/2], [2], -4*log(1-x)) = 1/(1-x)^2*(BesselI(0, 2*log(1-x))+BesselI(1, 2*log(1-x))). a(n)=(1/(2*pi))*int(product(x+k,k,0,n-1)*sqrt((4-x)/x),x,0,4) (moment representation). [Paul Barry, Jul 26 2010] MATHEMATICA CoefficientList[Series[(BesselI[0, 2*Log[1-x]] + BesselI[1, 2*Log[1-x]]) / (1-x)^2, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Mar 02 2014 *) Table[Sum[Abs[StirlingS1[n, k]]*Binomial[2*k, k]/(k+1), {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 02 2014 *) PROG (PARI) a(n)=sum(k=0, n, abs(stirling(n, k, 1)) * binomial(2*k, k)/(k+1) ); \\ Joerg Arndt, Mar 02 2014 CROSSREFS Cf. A000108, A008275, A064856. Sequence in context: A188051 A247230 A047159 * A293195 A090754 A067764 Adjacent sequences:  A086659 A086660 A086661 * A086663 A086664 A086665 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Sep 12 2003 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.

Last modified November 29 23:37 EST 2020. Contains 338780 sequences. (Running on oeis4.)