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A064428
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Number of partitions of n with nonnegative crank.
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1
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1, 0, 1, 2, 3, 4, 6, 8, 12, 16, 23, 30, 42, 54, 73, 94, 124, 158, 206, 260, 334, 420, 532, 664, 835, 1034, 1288, 1588, 1962, 2404, 2953, 3598, 4392, 5328, 6466, 7808, 9432, 11338, 13632, 16326, 19544, 23316, 27806, 33054, 39273, 46534, 55096, 65076, 76808
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| For a partition p, let l(p) = largest part of p, w(p) = number of 1's in p, m(p) = number of parts of p larger than w(p). The crank of p is given by l(p) if w(p) = 0, otherwise m(p)-w(p).
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REFERENCES
| B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 18 Entry 9 Corollary (i).
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FORMULA
| a(n) = (A000041(n)+A064410(n))/2, n>1.
G.f.: (Sum_{k>=0} (-1)^k*x^(k(k+1)/2))/(Product_{k>0} 1-x^k). - Michael Somos, Jul 28 2003
G.f.: 1 + sum(i=1, oo, x^(i(i+1))/product(j=1, i, (1-x^j)^2)) - Jon Perry (perry(AT)globalnet.co.uk), Jul 18 2004
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PROG
| (PARI) a(n)=if(n<0, 0, polcoeff(sum(k=0, (sqrtint(1+8*n)-1)\2, (-1)^k*x^((k+k^2)/2))/eta(x+x*O(x^n)), n))
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CROSSREFS
| Cf. A064391, A000041, A064410.
Sequence in context: A046682 A005987 A125895 * A052810 A079647 A164090
Adjacent sequences: A064425 A064426 A064427 * A064429 A064430 A064431
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KEYWORD
| nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 30 2001
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