A014481 a(n) = 2^n*n!*(2*n+1).

1, 6, 40, 336, 3456, 42240, 599040, 9676800, 175472640, 3530096640, 78033715200, 1880240947200, 49049763840000, 1377317368627200, 41421544567603200, 1328346084409344000, 45249466617298944000, 1631723190138961920000

Offset

0,2

Comments

Denominators of expansion of Integral_{t=0..x} exp(-(t^2)/2) dt = sqrt(Pi/2)*erf(x/sqrt(2)) in powers x^(2*n+1), n >= 0. Numerators are (-1)^n. - Wolfdieter Lang, Jun 29 2007

a(n) = A009445(n) / A001147(n). - Reinhard Zumkeller, Dec 03 2011

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Eric Weisstein's World of Mathematics, Normal Distribution Function

Index entries for sequences related to factorial numbers

Formula

Expansion of (1+2x)/(1-2x)^2.

G.f.: G(0)/(2*x) - 1/x, where G(k)= 1 - 2*x+ 1/(1 - 2*x*(k+1)/(2*x*(k+1) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 24 2013

From Amiram Eldar, Jul 31 2020: (Start)

Sum_{n>=0} 1/a(n) = sqrt(Pi/2) * erfi(1/sqrt(2)).

Sum_{n>=0} (-1)^n/a(n) = sqrt(Pi/2) * erf(1/sqrt(2)). (End)

Prog

(Magma) [2^n*Factorial(n)*(2*n+1): n in [0..50]]; // Vincenzo Librandi, Apr 25 2011
(Haskell)
a014481 n = a009445 n `div` a001147 n  -- Reinhard Zumkeller, Dec 03 2011

Crossrefs

From Johannes W. Meijer, Nov 12 2009: (Start)

Appears in A167572.

Equals row sums of A167583.

(End)

Sequence in context: A231126 A341587 A006387 * A184266 A000683 A352357

Adjacent sequences: A014478 A014479 A014480 * A014482 A014483 A014484

Keyword

nonn

Author

N. J. A. Sloane

Status

approved