A261047 - OEIS

%I #7 Jul 28 2017 08:51:10

%S 1,2,9,40,212,1248,8400,63576,540858,5132564,53952742,623324184,

%T 7855144818,107224120980,1575511525794,24784246515256,415435624535225,

%U 7389692971336602,138992875726543381,2755750468146310688,57433108983590606292

%N Euler transform of (n+1)!.

%F a(n) ~ (n+1)! * (1 + 2/n + 7/n^2 + 33/n^3 + 219/n^4 + 1705/n^5 + 15707/n^6 + 166289/n^7 + 1993141/n^8 + 26727125/n^9 + 397081369/n^10).

%F a(n) ~ n! * n * (1 + 3/n + 9/n^2 + 40/n^3 + 252/n^4 + 1924/n^5 + 17412/n^6 + 181996/n^7 + 2159430/n^8 + 28720266/n^9 + 423808494/n^10).

%p a:= proc(n) option remember; `if`(n=0, 1, add(add(d*

%p      (d+1)!, d=numtheory[divisors](j))*a(n-j), j=1..n)/n)

%p     end:

%p seq(a(n), n=0..30);  # _Alois P. Heinz_, Jul 28 2017

%t nmax=20; CoefficientList[Series[Product[1/(1-x^k)^((k+1)!), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A107895, A179327.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Aug 08 2015