A339034 - OEIS

%I #16 Feb 01 2024 01:55:15

%S 1,1,4,11,35,147,805,5399,42273,375787,3728261,40788255,487539769,

%T 6319430483,88272658797,1321745733511,21117967813025,358591883025339,

%U 6448525343069653,122424951294889967,2446864618294774281,51354975368171586595,1129258990476358286909

%N Row sums of A339033.

%H Paolo Xausa, <a href="/A339034/b339034.txt">Table of n, a(n) for n = 0..440</a>

%F a(n) = n! - (n - 1)! + Sum_{k=1..n} (n + 1 - k)*(k - 1)! for n > 0.

%t A339034[n_] := If[n == 0, 1, n! + Sum[(n+1-k)*(k-1)!, {k, n-1}]];

%t Array[A339034, 25, 0] (* _Paolo Xausa_, Jan 31 2024 *)

%o (SageMath)

%o def A339034(n):

%o     if n == 0: return 1

%o     d = factorial(n) - factorial(n - 1)

%o     return add((n + 1 - k)*factorial(k - 1) for k in (1..n)) + d

%o print([A339034(n) for n in (0..22)])

%o (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 Cf. A339033.

%K nonn

%O 0,3

%A _Peter Luschny_, Nov 20 2020