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a(n) = Sum_{k=0..n} k^(2*n) * Stirling1(n,k).
4

%I #13 Feb 04 2022 11:55:49

%S 1,1,15,539,28980,1295404,-177715720,-88870557952,-11213754156480,

%T 11072302541223336,8352732988619491824,-1800044600955923261688,

%U -8483589341410812834791040,-2945489916041839476122254560

%N a(n) = Sum_{k=0..n} k^(2*n) * Stirling1(n,k).

%F E.g.f.: Sum_{k>=0} log(1 + k^2*x)^k / k!.

%o (PARI) a(n) = sum(k=0, n, k^(2*n)*stirling(n, k, 1));

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, log(1+k^2*x)^k/k!)))

%Y Cf. A229261, A320082, A351133, A351180, A351182.

%K sign

%O 0,3

%A _Seiichi Manyama_, Feb 04 2022