|
| |
|
|
A002690
|
|
a(n) = (n+1) * (2*n)! / n!.
(Formerly M3665 N1491)
|
|
4
|
|
|
|
1, 4, 36, 480, 8400, 181440, 4656960, 138378240, 4670265600, 176432256000, 7374868300800, 337903056691200, 16838835658444800, 906706535454720000, 52459449551308800000, 3245491278907637760000, 213796737998040637440000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
Coefficients of orthogonal polynomials.
E.g.f. for series with alternating signs: x/(1+4*x)^(1/2).
Central terms of triangle A245334. - Reinhard Zumkeller, Aug 30 2014
|
|
|
REFERENCES
|
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
|
Vincenzo Librandi, Table of n, a(n) for n = 0..200
H. E. Salzer, Orthogonal polynomials arising in the evaluation of inverse Laplace transforms, Math. Comp. 9 (1955), 164-177.
H. E. Salzer, Orthogonal polynomials arising in the evaluation of inverse Laplace transforms, Math. Comp. 9 (1955), 164-177. [Annotated scanned copy]
|
|
|
FORMULA
|
E.g.f.: (1-2*x)/(1-4*x)^(3/2).
|
|
|
MAPLE
|
with(combstruct):bin := {B=Union(Z, Prod(B, B))}: seq (count([B, bin, labeled], size=n)*n, n=1..17); # Zerinvary Lajos, Dec 05 2007
|
|
|
MATHEMATICA
|
Table[((n+1)(2n)!)/n!, {n, 0, 20}] (* Harvey P. Dale, Sep 04 2011 *)
|
|
|
PROG
|
(PARI) a(n)=(n+1)*(2*n)!/n!
(Magma) [(n+1) * Factorial(2*n) /Factorial(n): n in [0..20]]; // Vincenzo Librandi, Sep 05 2011
(Haskell)
a002690 n = a245334 (2 * n) n -- Reinhard Zumkeller, Aug 30 2014
|
|
|
CROSSREFS
|
a(n) = (n+1) * A001813(n) = 2^n * A001193(n+1).
Cf. A002691, A000407.
Cf. A245334.
Sequence in context: A135906 A197446 A291313 * A094417 A349504 A354264
Adjacent sequences: A002687 A002688 A002689 * A002691 A002692 A002693
|
|
|
KEYWORD
|
nonn,easy,nice
|
|
|
AUTHOR
|
N. J. A. Sloane
|
|
|
EXTENSIONS
|
Edited by Ralf Stephan, Mar 21 2004
|
|
|
STATUS
|
approved
|
| |
|
|
