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

0,3

Links

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

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A339033.

Sequence in context: A349185 A358826 A212910 * A114248 A149237 A054577

Adjacent sequences: A339031 A339032 A339033 * A339035 A339036 A339037

Keyword

nonn

Author

Peter Luschny, Nov 20 2020

Status

approved