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A187655
Self-convolution of the central Stirling numbers of the second kind.
3
1, 2, 15, 194, 3631, 89712, 2764268, 102207394, 4411265695, 217707856946, 12092696127691, 746552539553152, 50708165735187572, 3757864633323765824, 301719332111553586612, 26089939284112306045362, 2417245528055399202851119
OFFSET
0,2
COMMENTS
The sequence of the central Stirling numbers of the second kind is 1, 1, 7, 90, 1701,... with offset 0 (see A007820).
FORMULA
a(n) = sum_{k=0..n} A048993(2k,k)*A048993(2n-2k,n-k).
a(n) ~ 2^(2*n+1/2) * n^(n-1/2) / (sqrt(Pi*(1-c)) * exp(n) * (c*(2-c))^n), where c = -LambertW(-2*exp(-2)) = 0.4063757399599599... . - Vaclav Kotesovec, May 20 2014
MAPLE
seq( add(combinat[stirling2](2*k, k) *combinat[stirling2](2*(n-k), n-k) , k=0..n), n=0..12);
MATHEMATICA
Table[Sum[StirlingS2[2k, k]StirlingS2[2n - 2k, n - k], {k, 0, n}], {n, 0, 16}]
PROG
(Maxima) makelist(sum(stirling2(2*k, k)*stirling2(2*n-2*k, n-k), k, 0, n), n, 0, 12);
CROSSREFS
Cf. A187656.
Sequence in context: A374866 A127090 A198522 * A046249 A042355 A208467
KEYWORD
nonn,easy
AUTHOR
Emanuele Munarini, Mar 12 2011
STATUS
approved