A261047 Euler transform of (n+1)!.

1, 2, 9, 40, 212, 1248, 8400, 63576, 540858, 5132564, 53952742, 623324184, 7855144818, 107224120980, 1575511525794, 24784246515256, 415435624535225, 7389692971336602, 138992875726543381, 2755750468146310688, 57433108983590606292

Offset: 0

Author

Vaclav Kotesovec, Aug 08 2015

Keywords

• nonn

Crossrefs

Cf. A107895, A179327.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(add(d*
     (d+1)!, d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Jul 28 2017

Mathematica

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

Formula

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).

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).