A339034 Row sums of A339033.

1, 1, 4, 11, 35, 147, 805, 5399, 42273, 375787, 3728261, 40788255, 487539769, 6319430483, 88272658797, 1321745733511, 21117967813025, 358591883025339, 6448525343069653, 122424951294889967, 2446864618294774281, 51354975368171586595, 1129258990476358286909

Offset: 0

Author

Peter Luschny, Nov 20 2020

Keywords

• nonn

Links

• Paolo Xausa, Table of n, a(n) for n = 0..440

Crossrefs

Cf. A339033.

Programs

Mathematica

A339034[n_] := If[n == 0, 1, n! + Sum[(n+1-k)*(k-1)!, {k, n-1}]];
Array[A339034, 25, 0] (* Paolo Xausa, Jan 31 2024 *)

PARI

a(n) = if (n==0, 1, n! - (n-1)! + sum(k=1, n, (n+1-k)*(k-1)!)); \\ Michel Marcus, Dec 02 2020

SageMath

def A339034(n):
    if n == 0: return 1
    d = factorial(n) - factorial(n - 1)
    return add((n + 1 - k)*factorial(k - 1) for k in (1..n)) + d
print([A339034(n) for n in (0..22)])

Formula

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