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%I #11 Sep 08 2022 08:44:57
%S 1,1,3,40,1015,40631,2334766,180836664,18067408311,2254675244287,
%T 342877692847261,62311687363814736,13318714515734069806,
%U 3304254169559017642774,940912768920331123369272,304601441677789509306775856
%N a(n) = Sum_{k=0..n} C(n,k)*Stirling1(n,k)^2.
%H G. C. Greubel, <a href="/A047799/b047799.txt">Table of n, a(n) for n = 0..245</a>
%p seq(add(binomial(n,k)*stirling1(n, k)^2, k = 0..n), n = 0..20); # _G. C. Greubel_, Aug 07 2019
%t Table[Sum[Binomial[n, k]*StirlingS1[n, k]^2, {k, 0, n}], {n,0,20}] (* _G. C. Greubel_, Aug 07 2019 *)
%o (PARI) {a(n) = sum(k=0,n, binomial(n,k)*stirling(n,k,1)^2)};
%o vector(20, n, n--; a(n)) \\ _G. C. Greubel_, Aug 07 2019
%o (Magma) [(&+[Binomial(n,k)*StirlingFirst(n,k)^2: k in [0..n]]): n in [0..20]]; // _G. C. Greubel_, Aug 07 2019
%o (Sage) [sum(binomial(n,k)*stirling_number1(n,k)^2 for k in (0..n)) for n in (0..20)] # _G. C. Greubel_, Aug 07 2019
%o (GAP) List([0..20], n-> Sum([0..n], k-> Binomial(n,k)*Stirling1(n,k)^2 )) # _G. C. Greubel_, Aug 07 2019
%Y Cf. A008275, A047798, A122455.
%K nonn
%O 0,3
%A _N. J. A. Sloane_
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