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A007403
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Sum_{m=0..n} (Sum_{k=0..m} C(n,k))^3 = (n+2)*2^(3*n-1)-3*2^(n-2)*n*binomial(2*n,n).
(Formerly M4656)
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0
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1, 9, 92, 920, 8928, 84448, 782464, 7130880, 64117760, 570166784, 5023524864, 43915595776, 381350330368, 3292451880960, 28283033157632, 241884640182272, 2060565937127424, 17492250190544896, 148027589475696640
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| G. E. Andrews and P. Paule, MacMahon's partition analysis. IV. Hypergeometric multisums. In The Andrews Festschrift (Maratea, 1998). Sem. Lothar. Combin. 42 (1999), Art. B42i, 24 pp.
N. J. Calkin, A curious binomial identity, Discr. Math., 131 (194), 335-337.
M. Hirschhorn, Calkin's binomial identity, Discr. Math., 159 (1996), 273-278.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Jun Wang and Zhizheng Zhang, On extensions of Calkin's binomial identities, Discrete Math., 274 (2004), 331-342.
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FORMULA
| G.f.: (1-(4+3*Sqrt[1-8*x])*x)/(1-8*x)^2 [From Harvey P. Dale, June 30 2011]
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MAPLE
| f:=n->n*8^n/2+8^n-(3*n/4)*2^n*binomial(2*n, n);
[seq(f(n), n=0..50)];
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MATHEMATICA
| Table[(n+2)2^(3n-1)-3 2^(n-2)n Binomial[2n, n], {n, 0, 20}] (* From Harvey P. Dale, June 30 2011 *)
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CROSSREFS
| Sequence in context: A034666 A022505 A164913 * A015587 A024117 A076456
Adjacent sequences: A007400 A007401 A007402 * A007404 A007405 A007406
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein
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