1,2

a(n)=determinant of M(2n-1) where M(k) is the k X k matrix with m(i,j)=j if i+j=k m(i,j)=i otherwise.

(-1)^n*a(n)/2^(2n-1) is the permanent of the (m x m) matrix {1/(x_i-y_j), 1<=i<=m, 1<=j<=m}, where x_1,x_2,...,x_m are the zeros of x^m-1 and y_1,y_2,...,y_m the zeros of y^m+1 and m=2n-1.

Eric Weisstein's World of Mathematics, Struve function

G.-N. Han and C. Krattenthaler, Rectangular Scott-type permanents

a(n+1)=(4n^2-1)*a(n)

E.g.f.: 1/(1-x^2)^(3/2) (with interpolated zeros). - Paul Barry (pbarry(AT)wit.ie), May 26 2003

(2n-1)! * C(2n-2, n-1) / 2^(2n-2). - R. Stephan, Mar 22 2004.

Alternatingly signed values have e.g.f. sqrt(1+x^2).

a(n) is the value of the n-th moment of : 1/Pi BesselK(1, sqrt(x)) on the positive part of the real line. [From Olivier GERARD (olivier.gerard(AT)gmail.com), May 20 2009]

M(5) is /1, 2, 3, 1, 5/ 1, 2, 2, 4, 5/ 1, 3, 3, 4, 5/ 4, 2, 3, 4, 5/ 1, 2, 3, 4, 5/

int( x^3 besselK(1, sqrt(x)), x=0..infty) = 1575 Pi. [From Olivier GERARD (olivier.gerard(AT)gmail.com), May 20 2009]

Cf. A001818, A000165.

Bisection of A000246, A053195, |A013069|, |A046126|. Cf. A000909.

Cf. A001044, A010791, |A129464|, A114779, are also values of similar moments. [From Olivier GERARD (olivier.gerard(AT)gmail.com), May 20 2009]

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 27 2009: (Start)

Equals the row sums of A162005.

(End)

Sequence in context: A144949 A144950 A144951 this_sequence A012494 A012780 A072503

Adjacent sequences: A079481 A079482 A079483 this_sequence A079485 A079486 A079487

nonn

Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 17 2003

Simpler description from Daniel Flath (deflath(AT)yahoo.com), Mar 05 2004