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Search: id:A092885
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| A092885 |
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Number of partitions of n in which no parts are multiples of 25. |
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+0
3
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| 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627, 792, 1002, 1255, 1575, 1957, 2435, 3008, 3715, 4560, 5597, 6831, 8334, 10121, 12280, 14841, 17921, 21560, 25914, 31050, 37162, 44352, 52877, 62876, 74685, 88507
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Euler transform of period 25 sequence [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,...].
Expansion of q^(-1)eta(q^25)/eta(q) in powers of q.
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REFERENCES
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T. Horie and N. Kanou, Certain modular functions similar to the Dedekind eta function, Abh. Math. Sem. Univ. Hamburg 72 (2002), 89-117. MR1941549 (2003j:11043)
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FORMULA
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Given g.f. A(x), then B(x)=x*A(x) satisfies 0=f(B(x), B(x^2)) where f(u, v)= u^3 +v^3 -5*(u*v)^2 -2*u*v*(u+v) -u*v.
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PROGRAM
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(PARI) a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff(eta(x^25+A)/eta(x+A), n))
(PARI) {a(n)=local(A, m); if(n<0, 0, n++; m=5; A=x+O(x^6); while(m<n, m*=5; A=x*subst((A* (1-2*A+4*A^2-3*A^3+A^4)/ (1+3*A+4*A^2+2*A^3+A^4)/ x)^(1/5), x, x^5)); polcoeff(1/(1/A-A-1), n))}
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CROSSREFS
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Sequence in context: A008635 A008641 A046054 this_sequence A000041 A084251 A024794
Adjacent sequences: A092882 A092883 A092884 this_sequence A092886 A092887 A092888
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Mar 10 2004
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