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A107895 Euler transform of n!. 10
1, 1, 3, 9, 36, 168, 961, 6403, 49302, 430190, 4199279, 45326013, 535867338, 6884000262, 95453970483, 1420538043009, 22579098396600, 381704267100888, 6837775526561031, 129377310771795789, 2578101967764973314, 53965231260126083854, 1183813954026245944519 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..170

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-Fran├žois Alcover, Feb 25 2014, after Alois P. Heinz *)

CROSSREFS

Cf. A077365, A107894, A179327, A248871, A261047.

Sequence in context: A156016 A032314 A144352 * A237653 A070960 A030834

Adjacent sequences:  A107892 A107893 A107894 * A107896 A107897 A107898

KEYWORD

nonn

AUTHOR

Thomas Wieder, May 26 2005

STATUS

approved

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Last modified November 20 12:37 EST 2018. Contains 317402 sequences. (Running on oeis4.)