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A002370
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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)
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1
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1, 1, 6, 120, 5250, 395010, 45197460, 7299452160, 1580682203100, 441926274289500, 154940341854097800, 66565404923242024800, 34389901168124209507800, 21034386936107260971255000, 15032296693671903309613950000, 12411582569784462888618434640000
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OFFSET
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0,3
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REFERENCES
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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).
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LINKS
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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.
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FORMULA
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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.
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MAPLE
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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);
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PROG
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(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 */
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CROSSREFS
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Cf. A167028.
Sequence in context: A094273 A094278 A093910 * A012846 A012641 A012795
Adjacent sequences: A002367 A002368 A002369 * A002371 A002372 A002373
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Jon E. Schoenfield (jonscho(AT)hiwaay.net), Mar 24 2010
Edited by Alois P. Heinz, Jan 21 2011
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STATUS
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approved
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