A277407 a(n) = A277406(n)/(n+1).

1, 1, 3, 19, 220, 4196, 120876, 4915212, 268194816, 18903020544, 1671209210880, 181064295924480, 23589442167333120, 3638090042721918720, 655483159341216541440, 136420837710333144595200, 32478481518550347674419200, 8770206330674425311097651200, 2666047809138871800854163456000, 906320525390421790143785781657600, 342508343836409428996994343026688000

Offset: 0

Author

Paul D. Hanna, Oct 16 2016

Keywords

• nonn

Comments

A277406(n) equals the sum of all permutations of compositions of functions (1 + k*x) for k=1..n, evaluated at x=1.

Crossrefs

Cf. A277405, A277406.

Programs

PARI

{a(n) = 1/(n+1) * sum(k=0, n, k!*(n-k)! * sum(i=0, n-k+1, (-1)^(n-i+1) * stirling(i, n-k+1, 2) * stirling(n+1, i, 1)))}
for(n=0, 20, print1(a(n), ", "))

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} k!*(n-k)! * Sum_{i=0..n-k+1} (-1)^(n-i+1) * Stirling2(i,n-k+1) * Stirling1(n+1,i).