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Search: id:A091200
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| A091200 |
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G.f. A(x) satisfies xA(x)^5 = B(xA(x^5)) where B(x) = x/(1-5x). |
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+0
3
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| 1, 1, 3, 11, 44, 185, 802, 3553, 15994, 72886, 335387, 1555487, 7261310, 34083382, 160730900, 761039051, 3616102911, 17235223345, 82372594183, 394648349447, 1894921311499, 9116598414141, 43939539520427, 212124129983285
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OFFSET
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0,3
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COMMENT
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More generally, given A(x) satisfies xA(x)^p = B(xA(x^p)) where B(x) = x/(1-p*x), then it appears that A(x) is an integer series only when p is prime. This is a special case of sequences with g.f.s that satisfy the more general functional equation xA(x)^m = B(xA(x^m)) originated by Michael Somos; some other examples are A085748, A091188, and A091190.
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PROGRAM
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(PARI) {a(n)=local(A, m); p=5; if(n<0, 0, m=1; A=1+O(x); while(m<=n, m*=p; A=x*subst(A, x, x^p); A=(A/(1-p*A)/x)^(1/p)); polcoeff(A, n))}
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CROSSREFS
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Cf. A085748, A091188, A091190.
Adjacent sequences: A091197 A091198 A091199 this_sequence A091201 A091202 A091203
Sequence in context: A026748 A113174 A132840 this_sequence A127632 A061706 A121220
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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), Feb 23 2004
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