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%I #23 Oct 10 2023 05:24:14
%S 1,15,301,7770,246730,9321312,408741333,20415995028,1144614626805,
%T 71187132291275,4864251308951100,362262620784874680,
%U 29206898819153109600,2534474684137526739000,235535731151727520125765,23339590705557273894321960
%N a(n) = Stirling2(2*n+1, n).
%H G. C. Greubel, <a href="/A247238/b247238.txt">Table of n, a(n) for n = 1..340</a>
%F a(n) = A243227(n) / (n-1)!. - _Vaclav Kotesovec_, Nov 29 2014
%F a(n) ~ 2^(2*n+1/2) * n^(n+1/2) / (sqrt(Pi) * sqrt(1-c) * exp(n) * c^n * (2-c)^(n+1)), where c = -LambertW(-2*exp(-2)) = 0.4063757399599599... (see A226775). - _Vaclav Kotesovec_, Nov 29 2014
%F O.g.f. Sum_{n>=1} n^(2*n+1) * x^n * exp(-n^2*x) / n! = Sum_{n>=1} a(n)*x^n. - _Paul D. Hanna_, Oct 09 2023
%e O.g.f.: A(x) = x + 15*x^2 + 301*x^3 + 7770*x^4 + 246730*x^5 + 9321312*x^6 + ... where A(x) = 1^3*x*exp(-1^2*x) + 2^5*exp(-2^2*x)*x^2/2! + 3^7*exp(-3^2*x)*x^3/3! + 4^9*exp(-4^2*x)*x^4/4! + 5^11*exp(-5^2*x)*x^5/5! + ...
%t Table[StirlingS2[2*n+1, n], {n, 1, 20}] (* _Vaclav Kotesovec_, Nov 29 2014 *)
%o (PARI) vector(50, n, stirling(2*n+1, n, 2)) \\ _Colin Barker_, Nov 28 2014
%Y Cf. A048993, A007820, A217899, A243227, A226775.
%K nonn
%O 1,2
%A _Vladimir Kruchinin_, Nov 28 2014
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