login
A187647
Partial sums of the central Stirling numbers of the second kind.
1
1, 2, 9, 99, 1800, 44325, 1367977, 50697257, 2192461310, 108367857065, 6025952821720, 372308453692006, 25302513044450266, 1875871087298000326, 150658859151673309726, 13030526931922299349726, 1207492044401730133131811
OFFSET
0,2
LINKS
FORMULA
a(n) = sum_{k=0..n} A048993(2*k,k).
a(n+1)-a(n) = A007820(n+1).
a(n) ~ n^n * 2^(2*n) / (sqrt(2*Pi*(1-c)*n) * exp(n) * (2-c)^n * c^n), where c = -LambertW(-2*exp(-2)). - Vaclav Kotesovec, May 11 2014
MAPLE
seq(sum(combinat[stirling2](2*k, k), k=0..n), n=0..12);
MATHEMATICA
Table[Sum[StirlingS2[2k, k], {k, 0, n}], {n, 0, 16}]
PROG
(Maxima) makelist(sum(stirling2(2*k, k), k, 0, n), n, 0, 12);
CROSSREFS
Sequence in context: A027686 A360696 A357825 * A322645 A368725 A277180
KEYWORD
nonn,easy
AUTHOR
Emanuele Munarini, Mar 12 2011
STATUS
approved