A184975 Expansion of e.g.f. exp((1-sqrt(1-4*log(1+x)))/2).

1, 1, 2, 12, 106, 1330, 21188, 412496, 9471180, 250752012, 7519114872, 251898595344, 9324409750104, 377947150828728, 16648683024776112, 791945577071452608, 40457530872588060816, 2209174906291706917008, 128405210614917271843872, 7915238091104410779024576

Offset

0,3

Links

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

Formula

a(n) = Sum_{k=1..n} Sum_{i=0..(n-k)} (i+k-1)!*C(k+2*i-1, i+k-1)*Stirling1(n, i+k)/(k-1)!, n>0, a(0)=1.

a(n) ~ n^(n-1) / (sqrt(2)*exp(n-3/8)*(exp(1/4)-1)^(n-1/2)). - Vaclav Kotesovec, Jun 02 2013

Mathematica

CoefficientList[Series[Exp[(1-Sqrt[1-4*Log[1+x]])/2], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 02 2013 *)

Prog

(Maxima) a(n):=if n=0 then 1 else sum((sum(((i+k-1)!*binomial(k+2*i-1, i+k-1) *stirling1(n, i+k)), i, 0, n-k))/(k-1)!, k, 1, n);
(PARI) my(x='x+O('x^50)); Vec(serlaplace(exp((1-sqrt(1-4*log(1+x)))/2))) \\ G. C. Greubel, Jun 02 2017

Crossrefs

Sequence in context: A217801 A036077 A275765 * A268538 A319291 A265132

Adjacent sequences: A184972 A184973 A184974 * A184976 A184977 A184978

Keyword

nonn

Author

Vladimir Kruchinin, Nov 22 2011

Status

approved