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A113145
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Row 4 of table A113143; equal to INVERT of quartic (or 4-fold) factorials shifted one place right.
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1
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1, 1, 2, 8, 60, 708, 11428, 232756, 5704964, 163192820, 5331728964, 195776203764, 7978838333188, 357313060904692, 17438518614448580, 921145685670017012, 52355425184381107332, 3185815887918686343924, 206633438251087758833476
(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} 4^(k-j)*A111146(k, j).
a(0) = 1; a(n+1) = Sum_{k=0..n} a(k)*A007696(n-k).
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EXAMPLE
| A(x) = 1 + x + 2*x^2 + 8*x^3 + 60*x^4 + 708*x^5 +...
= 1/(1 - x - x^2 - 5*x^3 - 45*x^4 -...- A007696(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, 4*i+1))); return(polcoeff(A, n, X))}
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CROSSREFS
| Cf. A113143, A007696 (4-fold factorials).
Sequence in context: A053871 A052622 A001188 * A036794 A096121 A143217
Adjacent sequences: A113142 A113143 A113144 * A113146 A113147 A113148
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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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