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 A193479 G.f. A(x) satisfies: 1+x = Sum_{n>=0} A(x)^n/sf(n), where A(x) = Sum_{n>=1} a(n)*x^n/sf(n), and sf(n) = Product_{k=0..n} k! is the superfactorial of n (A000178). 1
 1, -1, 5, -121, 16199, -13857481, 86631572159, -4470597876144961, 2126428452257713430399, -10305779379533133607589385601, 557802385738943120790269629003660799, -366846102335019802908345392106358106684889601, 3169417347948517943104654704100947667168800468999705599 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS EXAMPLE A(x) = x - x^2/(1!*2!) + 5*x^3/(1!*2!*3!) - 121*x^4/(1!*2!*3!*4!) + 16199*x^5/(1!*2!*3!*4!*5!) - 13857481*x^6/(1!*2!*3!*4!*5!*6!) +...+ a(n)*x^n/sf(n) +... where 1+x = 1 + A(x) + A(x)^2/(1!*2!) + A(x)^3/(1!*2!*3!) + A(x)^4/(1!*2!*3!*4!) + A(x)^5/(1!*2!*3!*4!*5!) + A(x)^6/(1!*2!*3!*4!*5!*6!) +...+  A(x)^n/sf(n) +... and sf(n) = 0!*1!*2!*3!*...*(n-1)!*n!. PROG (PARI) {a(n)=local(A=sum(m=1, n-1, a(m)*x^m/prod(k=0, m, k!))+O(x^(n+2))); prod(k=0, n, k!)*polcoeff(1+x-sum(m=0, n, A^m/prod(k=0, m, k!)), n)} CROSSREFS Cf. A000178, A193478, A193440. Sequence in context: A012151 A012156 A290167 * A324089 A071171 A113906 Adjacent sequences:  A193476 A193477 A193478 * A193480 A193481 A193482 KEYWORD sign AUTHOR Paul D. Hanna, Jul 27 2011 STATUS approved

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Last modified August 11 10:15 EDT 2022. Contains 356065 sequences. (Running on oeis4.)