OFFSET
1,2
COMMENTS
r(n)=sum(A191578(n,k)*k!/(n!*(n-k)!)*a(k)/(2*k-1)!,k,1,n)=0, n>1. r(1)=1.
The central column of the Worpitzky triangle, a(n) = A028246(2n, n). Peter Luschny, Jul 17 2012
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..215
Vladimir Kruchinin, The method for obtaining expressions for coefficients of reverse generating functions, arXiv:1211.3244 [math.CO], 2012.
FORMULA
a(n) = (n-1)!*stirling2(2*n-1,n).
a(n) = (1/n)*sum{i=0..n}(-1)^(n-i)*binomial(n,i)*i^(2*n-1) - Peter Luschny, Jul 17 2012
O.g.f.: Sum_{n>=1} n^(2*n-2)*x^n/(1 + n^2*x)^n = Sum_{n>=1} a(n)*x^n. - Paul D. Hanna, Jan 06 2018
MATHEMATICA
a[n_] := (n-1)!*StirlingS2[2*n-1, n]; Table[a[n], {n, 1, 14}] (* Jean-François Alcover, Feb 21 2013, from 1st formula *)
PROG
(Maxima) a(n)=(n-1)!*stirling2(2*n-1, n);
(Sage)
def A185157(n) :
return (1/n)*add((-1)^(n-i)*binomial(n, i)*i^(2*n-1) for i in (0..n))
[A185157(n) for n in (1..14)] # Peter Luschny, Jul 17 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Jan 23 2012
STATUS
approved