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 A113144 Row 3 of table A113143; equal to INVERT of triple (or 3-fold) factorials shifted one place right. 1
 1, 1, 2, 7, 41, 364, 4409, 67573, 1248626, 26948347, 664414997, 18409263772, 566018365445, 19117946453041, 703533848468330, 28013710891743007, 1199943043040160401, 55013996422974758476, 2687888298887895948065, 139414898768304344206141 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..19. FORMULA a(n) = Sum_{j=0..k} 3^(k-j)*A111146(k, j). a(0) = 1; a(n+1) = Sum_{k=0..n} a(k)*A007559(n-k). G.f.: 1/(Q(0)-x) where Q(k) = 1 - x*(3*k+1)/( 1 - x*(3*k+3)/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Mar 21 2013 EXAMPLE A(x) = 1 + x + 2*x^2 + 7*x^3 + 41*x^4 + 364*x^5 + 4409*x^6 +... = 1/(1 - x - x^2 - 4*x^3 - 28*x^4 -...- A007559(n)*x^(n+1) -...). PROG (PARI) {a(n)=local(x=X+X*O(X^n)); A=1/(1-x-x^2*sum(j=0, n, x^j*prod(i=0, j, 3*i+1))); return(polcoeff(A, n, X))} CROSSREFS Cf. A113143, A007559 (3-fold factorials). Sequence in context: A006677 A346271 A101390 * A320415 A006846 A047864 Adjacent sequences: A113141 A113142 A113143 * A113145 A113146 A113147 KEYWORD nonn AUTHOR Philippe Deléham and Paul D. Hanna, Oct 28 2005 STATUS approved

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Last modified October 3 11:12 EDT 2023. Contains 365861 sequences. (Running on oeis4.)