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Search: id:A071746
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| A071746 |
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p(7n+5)/7 where p(k) denotes the k-th partition number. |
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+0
2
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| 1, 11, 70, 348, 1449, 5334, 17822, 55165, 160215, 441105, 1159752, 2929465, 7142275, 16873472, 38749850, 86737678, 189672868, 405991500, 852077072, 1756048833, 3558408287, 7098041203, 13951818365, 27047831797, 51760979985
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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One of the congruences related to the partition numbers stated by Ramanujan.
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REFERENCES
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Berndt and Rankin, "Ramanujan: letters and commentaries", AMS-LMS, History of mathematics, vol. 9, pp. 192-193.
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FORMULA
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a(n) = (1/7)*A000041(7n+5)
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PROGRAM
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(PARI) a(n)=if(n<0, 0, n=7*n+5; polcoeff(1/eta(x+x*O(x^n)), n)/7)
(PARI) {a(n)=local(A, B); if(n<0, 0, A=x*O(x^n); B=eta(x^7+A); A=eta(x+A); polcoeff( B^3/A^4 +x*7*B^7/A^8, n))} /* Michael Somos Jan 01 2006 */
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CROSSREFS
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Cf. A017041, A071734, A076394.
Sequence in context: A066433 A038741 A099336 this_sequence A162568 A117047 A089720
Adjacent sequences: A071743 A071744 A071745 this_sequence A071747 A071748 A071749
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 24 2002
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