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A113144
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Row 3 of table A113143; equal to INVERT of triple (or 3-fold) factorials shifted one place right.
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1
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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; internal format)
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OFFSET
| 0,3
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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).
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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)
-...).
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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))}
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CROSSREFS
| Cf. A113143, A007559 (3-fold factorials).
Sequence in context: A087804 A006677 A101390 * A006846 A047864 A173916
Adjacent sequences: A113141 A113142 A113143 * A113145 A113146 A113147
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KEYWORD
| nonn
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr) and Paul D. Hanna (pauldhanna(AT)juno.com), Oct 28 2005
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