A343848 a(n) = Sum_{k = 0..n} (n - k)! LaguerreL(n - k, -k).

1, 2, 5, 17, 77, 444, 3123, 25933, 248163, 2687200, 32460889, 432482545, 6296217017, 99388128516, 1690073020687, 30788225809509, 597998944638879, 12332575195452440, 269072563350272149, 6190949611140562505, 149789737789559221397, 3801359947725801283196

Offset: 0

Author

Peter Luschny, May 08 2021

Keywords

• nonn

Crossrefs

Row sums of A343847.

Programs

Maple

A343848List := proc(n) local T; T := proc(n, k) option remember;
if n = k then return 1 elif n = k+1 then return k+1 fi;
(2*n-k-1)*T(n-1, k) - (n-k-1)^2*T(n-2, k) end:
seq(add(T(k, j), j = 0..k), k = 0..n) end: A343848List(21);

Mathematica

a[n_] := Sum[(n - k)! LaguerreL[n - k, -k], {k, 0, n}];
Table[a[n], {n, 0, 21}]

PARI

a(n) = sum(k=0, n, (n - k)!*sum(j=0, n - k, binomial(n - k, j) * k^j / j!))
for(n=0, 21, print(a(n)))

Formula

a(n) = Sum_{k=0..n} (n - k)! * Sum_{j=0..n-k} binomial(n - k, j) * k^j / j!.