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Search: id:A090351
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| A090351 |
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Satisfies A^3 = BINOMIAL(A^2). |
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+0
5
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| 1, 1, 3, 15, 108, 1032, 12388, 179572, 3052986, 59555338, 1310677726, 32114051862, 866766965308, 25547102523604, 816335926158372, 28107705687291892, 1037367351120788551, 40852168787823027351, 1709792654612819858341
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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)^3 = A(x/(1-x))^2/(1-x).
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EXAMPLE
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A^3 = BINOMIAL(A090352), since A090352=A^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^2, x, x/(1-x))/(1-x)+x*O(x^n); A=A-A^3+B); polcoeff(A, n, x))}
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CROSSREFS
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Cf. A084784, A090352, A090353, A090356, A090358.
Sequence in context: A074519 A105618 A120732 this_sequence A136221 A153305 A110328
Adjacent sequences: A090348 A090349 A090350 this_sequence A090352 A090353 A090354
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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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