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A129481
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a(n) = coefficient of x^n in n!*Product_{k=0..n} [Sum_{j=0..k} x^j/j! ].
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0
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1, 1, 3, 19, 175, 2111, 31321, 550810, 11194177, 258068893, 6653230111, 189653427206, 5922604033567, 201075967613262, 7373834652641003, 290474615891145106, 12232735359488840833, 548429151685677131389
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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EXAMPLE
| a(2) = [x^2] 2!*(1)*(1+x)*(1+x+x^2/2!) = [x^2] (2 +4*x +3*x^2 +x^3) = 3.
a(3) = [x^3] 3!*(1)*(1+x)*(1 + x + x^2/2!)*(1 + x + x^2/2! + x^3/3!) =
[x^3] (6 + 18*x + 24*x^2 + 19*x^3 +...) = 19.
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PROG
| (PARI) {a(n)=n!*polcoeff(prod(k=0, n, sum(j=0, k, x^j/j!)+x*O(x^n)), n)}
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CROSSREFS
| Sequence in context: A143768 A083071 A045531 * A156131 A161630 A121083
Adjacent sequences: A129478 A129479 A129480 * A129482 A129483 A129484
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Apr 17 2007
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