A259335 a(n) = Sum(b(2*n, k)^2*(b(2*n, k + 1) - b(2*n, k - 1)), k = 0 .. n)/(n*b(2*n, n)), where b denotes a binomial coefficient.

1, 7, 61, 611, 6686, 77729, 944245, 11859355, 152893720, 2013070126, 26967817306, 366542344117, 5043651762826, 70138959074461, 984384594022117, 13927418363218955, 198459156018467084, 2845950809029225472, 41044332341739034032, 594983281327999736694

Offset

1,2

Links

Table of n, a(n) for n=1..20.

H. W. Gould, Problem E2384, Amer. Math. Monthly, 79 (1972), p. 1034.

D. Zeitlin & N. J. A. Sloane, Correspondence, 1974 & 1991

Maple

f:=proc(n) local b;
b:=binomial;
add(b(2*n, k)^2*(b(2*n, k+1)-b(2*n, k-1)), k=0..n)/(n*b(2*n, n));
end;

Crossrefs

Sequence in context: A364430 A077642 A071172 * A127688 A111532 A061634

Adjacent sequences: A259332 A259333 A259334 * A259336 A259337 A259338

Keyword

nonn

Author

N. J. A. Sloane, Jun 25 2015

Status

approved