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Search: id:A090353
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| A090353 |
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Satisfies A^4 = BINOMIAL(A^3). |
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+0
6
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| 1, 1, 4, 28, 286, 3886, 66260, 1361972, 32784353, 904412593, 28124223808, 973106096392, 37073604836768, 1541948625066176, 69513081435903392, 3376138396206853792, 175739519606046355540, 9760024269508314079444
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OFFSET
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0,3
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COMMENT
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In general, if A^n = BINOMIAL(A^(n-1)), then for all integer m>0 there exists an integer sequence B such that B^d = BINOMIAL(A^m) where d=gcd(m+1,n). Also, coefficients of A(k*x)^n = k-th binomial transform of coefficients in A(k*x)^(n-1) for all k>0.
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FORMULA
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G.f. satisfies: A(x)^4 = A(x/(1-x))^3/(1-x).
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EXAMPLE
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A^4 = BINOMIAL(A090355), since A090355=A^3. Also, BINOMIAL(A) = A090354^2.
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PROGRAM
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(PARI) {a(n)=local(A); if(n<1, 0, A=1+x+x*O(x^n); for(k=1, n, B=subst(A^3, x, x/(1-x))/(1-x)+x*O(x^n); A=A-A^4+B); polcoeff(A, n, x))}
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CROSSREFS
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Cf. A084784, A090351, A090354, A090355, A090356, A090358.
Adjacent sequences: A090350 A090351 A090352 this_sequence A090354 A090355 A090356
Sequence in context: A007559 A138208 A071212 this_sequence A076729 A078634 A091485
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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), Nov 26 2003
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