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 A243435 O.g.f.: exp( Integral Sum_{n>=1} n! * n^(n-1) * x^(n-1) / Product_{k=1..n} (1 - k*n*x) dx ). 1
 1, 1, 3, 29, 686, 30552, 2191262, 230356646, 33349943718, 6359939775042, 1545000640114242, 465750550069828422, 170603300462464687996, 74630981535308266499848, 38429419191031108995080412, 23008323194727484508595195772, 15848730592891024979096686043722, 12445298391963001703710163766096546 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS EXAMPLE G.f.: A(x) = 1 + x + 3*x^2 + 29*x^3 + 686*x^4 + 30552*x^5 + 2191262*x^6 +... The logarithmic derivative equals the series: A'(x)/A(x) = 1/(1-x) + 2!*2*x/((1-2*x)*(1-4*x)) + 3!*3^2*x^2/((1-3*x)*(1-6*x)*(1-9*x)) + 4!*4^3*x^3/((1-4*x)*(1-8*x)*(1-12*x)*(1-16*x)) + 5!*5^4*x^4/((1-5*x)*(1-10*x)*(1-15*x)*(1-20*x)*(1-25*x)) +... Explicitly, the logarithm of the o.g.f. begins: log(A(x)) = x + 5*x^2/2 + 79*x^3/3 + 2621*x^4/4 + 149071*x^5/5 + 12954365*x^6/6 + 1596620719*x^7/7 + 264914218301*x^8/8 +... PROG (PARI) {a(n)=polcoeff(exp(intformal(sum(m=1, n+1, m!*m^(m-1)*x^(m-1)/prod(k=1, m, 1-m*k*x+x*O(x^n))))), n)} for(n=0, 30, print1(a(n), ", ")) CROSSREFS Cf. A084784, A243440. Sequence in context: A304553 A326337 A331389 * A064570 A117264 A256043 Adjacent sequences:  A243432 A243433 A243434 * A243436 A243437 A243438 KEYWORD nonn AUTHOR Paul D. Hanna, Jun 05 2014 STATUS approved

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Last modified May 13 02:36 EDT 2021. Contains 343836 sequences. (Running on oeis4.)