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Search: id:A131351
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| A131351 |
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G.f.: A(x) = 1 + Sum_{n>=1} x^n*[ Product_{k=1..n} F_k(x) ] where F_n(x) = 1 + x*F_n(x)^n. |
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1
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| 1, 1, 2, 4, 9, 24, 77, 295, 1329, 6924, 41030, 272271, 1996406, 16000511, 138953665, 1298206570, 12969761907, 137846434950, 1551712558368, 18429620298121, 230175973108212, 3014142623764514, 41275488455847862, 589698136493691293
(list; graph; listen)
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OFFSET
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0,3
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EXAMPLE
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A(x) = 1 + x + 2*x^2 + 4*x^3 + 9*x^4 + 24*x^5 + 77*x^6 + 295*x^7 +...
A(x) = 1 + x*F_1(x) + x^2*F_1(x)*F_2(x) + x^3*F_1(x)*F_2(x)*F_3(x) +...
where F_n(x) = Sum_{k>=0} C(n*k,k)/((n-1)*k + 1)*x^k:
F_1(x) = 1/(1-x);
F_2(x) = 1 + x + 2x^2 + 5x^3 + 14x^4 + 42x^5 + +... (A000108);
F_3(x) = 1 + x + 3x^2 + 12x^3 + 55x^4 + 273x^5 + ...(A001764);
F_4(x) = 1 + x + 4x^2 + 22x^3 + 140x^4 + 969x^5 +...(A002293); ...
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PROGRAM
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(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(k=0, n, A=1+x*A* Ser(vector(n+1, i, binomial((n-k+1)*(i-1), i-1)/((n-k)*(i-1)+1)))); polcoeff(A, n) }
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CROSSREFS
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Sequence in context: A091151 A093542 A000667 this_sequence A091352 A135934 A137154
Adjacent sequences: A131348 A131349 A131350 this_sequence A131352 A131353 A131354
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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), Jul 03 2007
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