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A339034 Row sums of A339033.

%I A339034 #16 Feb 01 2024 01:55:15
%S A339034 1,1,4,11,35,147,805,5399,42273,375787,3728261,40788255,487539769,
%T A339034 6319430483,88272658797,1321745733511,21117967813025,358591883025339,
%U A339034 6448525343069653,122424951294889967,2446864618294774281,51354975368171586595,1129258990476358286909
%N A339034 Row sums of A339033.
%H A339034 Paolo Xausa, <a href="/A339034/b339034.txt">Table of n, a(n) for n = 0..440</a>
%F A339034 a(n) = n! - (n - 1)! + Sum_{k=1..n} (n + 1 - k)*(k - 1)! for n > 0.
%t A339034 A339034[n_] := If[n == 0, 1, n! + Sum[(n+1-k)*(k-1)!, {k, n-1}]];
%t A339034 Array[A339034, 25, 0] (* _Paolo Xausa_, Jan 31 2024 *)
%o A339034 (SageMath)
%o A339034 def A339034(n):
%o A339034     if n == 0: return 1
%o A339034     d = factorial(n) - factorial(n - 1)
%o A339034     return add((n + 1 - k)*factorial(k - 1) for k in (1..n)) + d
%o A339034 print([A339034(n) for n in (0..22)])
%o A339034 (PARI) a(n) = if (n==0, 1, n! - (n-1)! + sum(k=1, n, (n+1-k)*(k-1)!)); \\ _Michel Marcus_, Dec 02 2020
%Y A339034 Cf. A339033.
%K A339034 nonn
%O A339034 0,3
%A A339034 _Peter Luschny_, Nov 20 2020