login
a(n) = Sum_{k=0..n} (k!)^(n+1) * binomial(n,k).
3

%I #12 May 05 2021 01:54:14

%S 1,2,11,1348,7993925,2986939982086,100308280020162672007,

%T 416336818263472141683094788104,

%U 281633775231427434285800695714399092181001,39594086714441777969538839399390619086007952991080833034

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

%H Seiichi Manyama, <a href="/A343929/b343929.txt">Table of n, a(n) for n = 0..29</a>

%F a(n) = [x^n] Sum_{k>=0} (k!)^(n+1) * x^k/(1 - x)^(k+1).

%F a(n) = n! * [x^n] exp(x) * Sum_{k>=0} (k!)^n * x^k.

%t a[n_] := Sum[(k!)^(n+1) * Binomial[n, k], {k, 0, n} ]; Array[a, 10, 0] (* _Amiram Eldar_, May 04 2021 *)

%o (PARI) a(n) = sum(k=0, n, k!^(n+1)*binomial(n, k));

%Y Cf. A046662, A343898, A343900, A343928.

%K nonn

%O 0,2

%A _Seiichi Manyama_, May 04 2021