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 A007841 Number of factorizations of permutations of n letters into cycles in nondecreasing length order. 41
 1, 1, 3, 11, 56, 324, 2324, 18332, 167544, 1674264, 18615432, 223686792, 2937715296, 41233157952, 623159583552, 10008728738304, 171213653641344, 3092653420877952, 59086024678203264, 1185657912197967744, 25015435198774723584, 552130504313534175744 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..450 Vaclav Kotesovec, Graph - The asymptotic ratio A. Knopfmacher, J. N. Ridley, Reciprocal sums over partitions and compositions, SIAM J. Discrete Math. 6 (1993), no. 3, 388-399. D. H. Lehmer, On reciprocally weighted partitions, Acta Arithmetica XXI (1972), 379-388. FORMULA E.g.f.: prod{m >= 1} 1/(1-x^m/m). a(n) = Sum_{k=1..n} (n-1)!/(n-k)!*b(k)*a(n-k), where b(k) = Sum_{d divides k} d^(1-k/d) and a(0) = 1. - Vladeta Jovovic, Oct 14 2002 a(n) = R(n,1), R(n,m) = R(n,m+1)+binomial(n,m)*(m-1)!*R(n-m,m), R(n,n)=(n-1)!, R(n,m)=0 for n=1} Sum_{j>=1} x^(j*k)/(k*j^k)). - Ilya Gutkovskiy, May 27 2018 MAPLE p := product(1/(1-x^m/m), m=1..100): s := series(p, x, 100): for i from 0 to 100 do printf(`%.0f, `, i!*coeff(s, x, i)) od: # second Maple program: with(combinat): b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(      (i-1)!^j*b(n-i*j, i-1)*multinomial(n, n-i*j, i\$j), j=0..n/i)))     end: a:= n-> b(n\$2): seq(a(n), n=0..30);  # Alois P. Heinz, Jul 21 2014 MATHEMATICA nmax = 25; CoefficientList[Series[1/Product[(1 - x^k/k), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jul 24 2019 *) nmax = 25; CoefficientList[Series[Exp[Sum[PolyLog[j, x^j]/j, {j, 1, nmax}]], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jul 24 2019 *) PROG (PARI) N=66; q='q+O('q^N); f=1/prod(n=1, N, 1-1/n*q^n ); egf=serlaplace(f); Vec(egf) /* Joerg Arndt, Oct 06 2012 */ (Maxima) R(n, m):=if n=0 then 1 else if n

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Last modified December 1 11:35 EST 2020. Contains 338833 sequences. (Running on oeis4.)