A367012 a(n) = Sum_{k=0..n} k! * (n-k)^k.

1, 1, 2, 5, 18, 95, 704, 6945, 87254, 1349603, 25064700, 548782229, 13970248610, 408882114519, 13625250384488, 512421111644105, 21577659567580014, 1010231138742981515, 52263989531636074964, 2971798406660674944573, 184850941269122564302010

Offset: 0

Author

Vaclav Kotesovec, Nov 01 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..315

Crossrefs

Cf. A005193, A026898, A367011.

Programs

Mathematica

Table[Sum[k! * (n-k)^k, {k, 0, n}], {n, 1, 20}]

PARI

a(n) = sum(k=0, n, k!*(n-k)^k); \\ Seiichi Manyama, Dec 31 2023

Formula

log(a(n)) ~ n*(2*log(n) - log(log(n)) - 2 - log(2) + log(2*log(n))/(2*log(n)) + 1/(8*log(n)^2)).

Extensions

a(0)=1 prepended by Seiichi Manyama, Dec 31 2023