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 A113133 a(0) = a(1) = 1, a(2) = x, a(3) = 2x^2, a(n) = x*(n-1)*a(n-1) + Sum_{j=2..n-2} (j-1)*a(j)*a(n-j), n>=4 and for x = 6. 6
 1, 1, 6, 72, 1332, 33264, 1040256, 38926656, 1692061488, 83688313536, 4638320578944, 284692939944192, 19169186341398912, 1404935464314299904, 111348880778746460160, 9489756817594314049536, 865470841829802331976448 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA a(n+1) = Sum{k, 0<=k<=n} 6^k*A113129(n, k). G.f.: A(x) = x/series_reversion(x*G(x)) where G(x) = g.f. of sextuple factorial numbers (A008542). G.f. satisfies: A(x*G(x)) = G(x) = g.f. of sextuple factorial numbers (A008542). EXAMPLE a(2) = 6. a(3) = 2*6^2 = 72. a(4) = 6*3*72 + 1*6*6 = 1332. a(5) = 6*4*1332 + 1*6*72 + 2*72*6 = 33264. a(6) = 6*5*33264 + 1*6*1332 + 2*72*72 + 3*1332*6 = 1040256. G.f.: A(x) = 1 + x + 6*x^2 + 72*x^3 + 1332*x^4 + 33264*x^5 +... = x/series_reversion(x + x^2 + 7*x^3 + 91*x^4 + 1729*x^5 +...). MATHEMATICA x=6; a[0]=a[1]=1; a[2]=x; a[3]=2x^2; a[n_]:=a[n]=x*(n-1)*a[n-1]+Sum[(j-1)*a[j ]*a[n-j], {j, 2, n-2}]; Table[a[n], {n, 0, 17}](Robert G. Wilson v) PROG (PARI) a(n)=Vec(x/serreverse(x*Ser(vector(n+1, k, if(k==1, 1, prod(j=0, k-2, 6*j+1))))))[n+1] (PARI) a(n, x=6)=if(n<0, 0, if(n==0 || n==1, 1, if(n==2, x, if(n==3, 2*x^2, x*(n-1)*a(n-1)+sum(j=2, n-2, (j-1)*a(j)*a(n-j)))))) CROSSREFS Cf. A008542, A075834(x=1), A111088(x=2), A113130(x=3), A113131(x=4), A113132(x=5), A113134(x=7), A113135(x=8). Sequence in context: A266869 A001763 A003235 * A302355 A089252 A052730 Adjacent sequences:  A113130 A113131 A113132 * A113134 A113135 A113136 KEYWORD nonn AUTHOR Philippe Deléham and Paul D. Hanna, Oct 28 2005 STATUS approved

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Last modified June 4 01:54 EDT 2020. Contains 334812 sequences. (Running on oeis4.)