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A107895
Euler transform of n!.
11
1, 1, 3, 9, 36, 168, 961, 6403, 49302, 430190, 4199279, 45326013, 535867338, 6884000262, 95453970483, 1420538043009, 22579098396600, 381704267100888, 6837775526561031, 129377310771795789, 2578101967764973314, 53965231260126083854, 1183813954026245944519
OFFSET
0,3
LINKS
FORMULA
a(n) ~ n! * (1 + 1/n + 3/n^2 + 12/n^3 + 66/n^4 + 450/n^5 + 3679/n^6 + 35260/n^7 + 388511/n^8 + 4844584/n^9 + 67502450/n^10), for next coefficients see A248871. - Vaclav Kotesovec, Mar 14 2015
G.f.: Product_{n>=1} 1/(1-x^n)^(n!). - Vaclav Kotesovec, Aug 04 2015
MAPLE
EulerTrans := proc(p) local b; b := proc(n) option remember; local d, j;
`if`(n=0, 1, add(add(d*p(d), d=numtheory[divisors](j)) *b(n-j), j=1..n)/n) end end:
A107895 := EulerTrans(n->n!): seq(A107895(n), n=0..20);
# After Alois P. Heinz, A000335. [Peter Luschny, Jul 07 2011]
MATHEMATICA
EulerTrans[p_] := Module[{b}, b[n_] := b[n] = Module[{d, j}, If[n == 0, 1, Sum[Sum[d*p[d], {d, Divisors[j]}]*b[n-j], {j, 1, n}]/n]]; b]; A107895 = EulerTrans[Factorial]; Table[A107895[n], {n, 0, 22}] (* Jean-François Alcover, Feb 25 2014, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Thomas Wieder, May 26 2005
STATUS
approved