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A125282
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G.f. satisfies: A(x) = Sum{n>=0} x^n * A(n*x).
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2
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1, 1, 2, 5, 17, 80, 525, 4839, 62936, 1158785, 30277579, 1124649526, 59465788597, 4480380804517, 481401971074410, 73812092299235769, 16158739669470307453, 5052972095683109687920, 2257981256268589345121153
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(n) = Sum_{k=0..n-1} (n-k)^k * a(k) for n>0 with a(0)=1.
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EXAMPLE
| A(x) = 1 + x + 2*x^2 + 5*x^3 + 17*x^4 + 80*x^5 + 525*x^6 + 4839*x^7 +...
G.f. A(x) satisfies:
A(x) = 1 + x*A(x) + x^2*A(2x) + x^3*A(3x) + x^4*A(4x) + x^5*A(5x) +...
which leads to the recurrence illustrated by:
a(4) = 4^0*(1) + 3^1*(1) + 2^2*(2) + 1^3*(5) = 17;
a(5) = 5^0*(1) + 4^1*(1) + 3^2*(2) + 2^3*(5) + 1^4*(17) = 80;
a(6) = 6^0*(1) + 5^1*(1) + 4^2*(2) + 3^3*(5) + 2^4*(17) + 1^5*(80) = 525.
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PROG
| (PARI) {a(n)=if(n==0, 1, sum(k=0, n-1, (n-k)^k*a(k)))}
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CROSSREFS
| Cf. A125281 (variant).
Sequence in context: A187245 A054499 A001186 * A020125 A076322 A098540
Adjacent sequences: A125279 A125280 A125281 * A125283 A125284 A125285
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Nov 29 2006
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