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1, 10, 126, 1716, 24310, 352716, 5200300, 77558760, 1166803110, 17672631900, 269128937220, 4116715363800, 63205303218876, 973469712824056, 15033633249770520, 232714176627630544, 3609714217008132870, 56093138908331422716, 873065282167813104916
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| The right-hand side of a binomial coefficient identity in H. W. Gould, Combinatorial Identities, Morgantown, 1982, (3.109), page 35.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
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FORMULA
| a(n)= A001700(2*n) = (n+1)*C(2*n+1), C(n) := A000108(n) (Catalan).
G.f.: (4-(1+4*y)*c(y)-(1-4*y)*c(-y))/(2*(1-(4*y)^2)) with y^2=x, c(y)= g.f. for A000108 (Catalan). - Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Dec 13 2001
a(n) ~ 2^(1/2)*pi^(-1/2)*n^(-1/2)*2^(4*n)*{1 - 5/16*n^-1 + ...} - Joe Keane (jgk(AT)jgk.org), Jun 11 2002
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MATHEMATICA
| Table[Binomial[4n+1, 2n], {n, 0, 30}] (* From Harvey P. Dale, Apr 04 2011 *)
4^Range[0, 22] Simplify[ CoefficientList[ Series[ Sqrt[2]/(((Sqrt[1 - 4 x] + 1)^(1/2))*Sqrt[1 - 4 x]), {x, 0, 22}], x]] (* Robert G. Wilson v, Aug 08 2011 *)
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CROSSREFS
| Cf. A000984, A001448.
Sequence in context: A097816 A079609 A101599 * A192600 A079241 A183538
Adjacent sequences: A002455 A002456 A002457 * A002459 A002460 A002461
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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