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A343900 a(n) = Sum_{k=0..n} (k!)^(k+1) * binomial(n,k).

%I A343900 #19 May 05 2021 01:55:02
%S A343900 1,2,11,1324,7967861,2986023826166,100306147958903465407,
%T A343900 416336313421816733159702737376,
%U A343900 281633758448076539969292901914477101456489,39594086612245054028213574779019294652734771094507399786
%N A343900 a(n) = Sum_{k=0..n} (k!)^(k+1) * binomial(n,k).
%C A343900 Binomial transform of (n!)^(n+1).
%H A343900 Seiichi Manyama, <a href="/A343900/b343900.txt">Table of n, a(n) for n = 0..29</a>
%F A343900 G.f.: Sum_{k>=0} (k!)^(k+1) * x^k/(1 - x)^(k+1).
%F A343900 E.g.f.: exp(x) * Sum_{k>=0} (k! * x)^k.
%t A343900 a[n_] := Sum[(k!)^(k+1) * Binomial[n, k], {k, 0, n}]; Array[a, 10, 0] (* _Amiram Eldar_, May 05 2021 *)
%o A343900 (PARI) a(n) = sum(k=0, n, k!^(k+1)*binomial(n, k));
%o A343900 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, k!^(k+1)*x^k/(1-x)^(k+1)))
%o A343900 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x)*sum(k=0, N, (k!*x)^k)))
%Y A343900 Cf. A000522, A036740, A046662, A091868, A343898, A343899, A343929.
%K A343900 nonn
%O A343900 0,2
%A A343900 _Seiichi Manyama_, May 03 2021