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Search: id:A090356
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| A090356 |
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Satisfies A^5 = BINOMIAL(A^4). |
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+0
5
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| 1, 1, 5, 45, 595, 10475, 231255, 6148495, 191276600, 6815243040, 273601200136, 12217471594856, 600580173151560, 32224787998758280, 1873909224391774760, 117388347849375956328, 7880739469498103077588, 564440024187816634143380
(list; graph; listen)
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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)^5 = A(x/(1-x))^4/(1-x).
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EXAMPLE
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A^5 = BINOMIAL(A090357), since A090357=A^4.
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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^4, x, x/(1-x))/(1-x)+x*O(x^n); A=A-A^5+B); polcoeff(A, n, x))}
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CROSSREFS
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Cf. A084784, A090353, A090357, A090358.
Sequence in context: A051539 A007696 A090136 this_sequence A112940 A085356 A113382
Adjacent sequences: A090353 A090354 A090355 this_sequence A090357 A090358 A090359
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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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