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A002370 a(n) = (2*n-1)^2 * a(n-1) - 3*C(2*n-1,3) * a(n-2) for n>1; a(0) = a(1) = 1.
(Formerly M4296 N1796)
2
1, 1, 6, 120, 5250, 395010, 45197460, 7299452160, 1580682203100, 441926274289500, 154940341854097800, 66565404923242024800, 34389901168124209507800, 21034386936107260971255000, 15032296693671903309613950000, 12411582569784462888618434640000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

A. C. Aitken, On the number of distinct terms in the expansion of symmetric and skew determinants, Edinburgh Math. Notes, No. 34 (1944), 1-5.

I. M. H. Etherington, Some problems of non-associative combinations, Edinburgh Math. Notes, 32 (1940), 1-6.

T. Muir, The Theory of Determinants in the Historical Order of Development. 4 vols., Macmillan, NY, 1906-1923, Vol. 3, p. 282.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=0..15.

T. Muir, The Theory of Determinants in the Historical Order of Development, 4 vols., Macmillan, NY, 1906-1923, Vol. 2.

FORMULA

a(n) = (2*n)! * [x^(2*n)] (1-x^2)^(-1/4)*exp(x^2/4).

a(n) = 2^n*GAMMA(n+1/2)*A002801(n)/Pi^(1/2) = GAMMA(n+1/2)*hypergeom([1/4, -n],[],-4)/Pi^(1/2) - Mark van Hoeij, Oct 26 2011.

MAPLE

a:= proc(n) option remember;

      `if` (n<2, 1, (2*n-1)^2 * a(n-1) -3*binomial(2*n-1, 3) *a(n-2))

    end:

seq (a(n), n=0..20);

MATHEMATICA

a[n_] := Gamma[n+1/2]*HypergeometricPFQ[{1/4, -n}, {}, -4]/Sqrt[Pi]; Table[a[n], {n, 0, 15}] (* Jean-Fran├žois Alcover, Mar 17 2014, after Mark van Hoeij *)

PROG

(PARI)

x='x+O('x^50);  v=Vec( (1-x)^(-1/4)*exp(x/4) );

vector(#v, n, v[n]*(2*n-2)! ) /* show terms */

CROSSREFS

Cf. A167028.

Sequence in context: A094273 A094278 A093910 * A012846 A012641 A012795

Adjacent sequences:  A002367 A002368 A002369 * A002371 A002372 A002373

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Jon E. Schoenfield, Mar 24 2010

Edited by Alois P. Heinz, Jan 21 2011

STATUS

approved

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Last modified September 20 04:05 EDT 2014. Contains 246983 sequences.