A256124
Coefficients in asymptotic expansion of sequence A107894.
Original entry on oeis.org
1, 1, 3, 12, 65, 443, 3626, 34811, 384479, 4806098, 67109281, 1035627571, 17505788792, 321689532755, 6385033369589, 136124555962844, 3102031758758001, 75238874818446123, 1935053096953675800, 52595740530868430967, 1506344153813275882667
Offset: 0
A107894(n) / n! ~ 1 + 1/n + 3/n^2 + 12/n^3 + 65/n^4 + 443/n^5 + 3626/n^6 + ...
A107895
Euler transform of n!.
Original entry on oeis.org
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
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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]
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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 *)
Showing 1-2 of 2 results.