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Search: id:A107716
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| A107716 |
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Inverse INVERT transform of triple factorial numbers (3*n-2)!!! (A007559). |
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+0
6
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| 1, 3, 21, 219, 2973, 49323, 964173, 21680571, 551173053, 15633866379, 489583062381, 16780438408539, 624935780160285, 25131869565110571, 1085528359404039117, 50124679063548821499, 2464153823558024331645
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OFFSET
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0,2
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COMMENT
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Column 0 of triangle A107717.
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FORMULA
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G.f.: A(x) = 1 - 1/[1 + Sum_{n>=1} (3*n-2)!!! * x^n ] where (3*n-2)!!! = Product_{k=0..n-1} (3*k+1).
a(n) = Sum_{k, 0<=k<=n} A089949(n, k)*3^k . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 15 2005
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EXAMPLE
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The triple factorials begin: {1,4,28,280,3640,58240,...}; thus the inverse INVERT transform of the triple factorials can be calculated by the g.f.s:
1/(1 + x + 4*x^2 + 28*x^3 + 280*x^4 + 3640*x^5 + 58240*x^6 +...) = (1 - x - 3*x^2 - 21*x^3 - 219*x^4 - 2973*x^5 - 49323*x^6 -...).
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PROGRAM
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(PARI) a(n)=polcoeff(1-(1+sum(k=1, n+1, prod(j=0, k-1, 3*j+1)*x^k)+x^2*O(x^n))^-1, n+1)
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CROSSREFS
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Cf. A007559, A000698, A107717.
Sequence in context: A088926 A120972 A158838 this_sequence A032033 A099121 A107864
Adjacent sequences: A107713 A107714 A107715 this_sequence A107717 A107718 A107719
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), May 23 2005
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