A093302 a(n) = (a(n-1)+(2n-1))*(2n) with a(0) = 0.

0, 2, 20, 150, 1256, 12650, 151932, 2127230, 34035920, 612646866, 12252937700, 269564629862, 6469551117240, 168208329048890, 4709833213369676, 141294996401091150, 4521439884834917792, 153728956084387206050

Offset

0,2

Links

Altug Alkan, Table of n, a(n) for n = 0..1000

Formula

a(n) = 2 * floor(e^(1/2) * n! * 2^n) - 2n - 2.

E.g.f.: (2x+4x^2)/(1-2x) * exp(x).

a(n) = 2*A271476(n) for n >= 1. - Altug Alkan, Aug 01 2018

Mathematica

RecurrenceTable[{a[0]==0, a[n]==(a[n-1]+2n-1)2n}, a, {n, 20}] (* Harvey P. Dale, May 20 2014 *)

Prog

(PARI) a(n)=2*floor(exp(1/2)*n!*2^n)-2*n-2
(PARI) x='x+O('x^99); concat(0, Vec(serlaplace((2*x+4*x^2)/(1-2*x)*exp(x)))) \\ Altug Alkan, Aug 01 2018
(PARI) a=vector(99); a[1]=2; for(n=2, #a, a[n] = 2*(a[n-1]+2*n-1)*n); concat(0, a) \\ Altug Alkan, Aug 01 2018

Crossrefs

a(n) = A007566(n)-1 = 2*A010844(n)-2n-2. Bisection of A077138.

Cf. A271476.

Sequence in context: A198647 A081159 A105489 * A248337 A270444 A093130

Adjacent sequences: A093299 A093300 A093301 * A093303 A093304 A093305

Keyword

easy,nonn

Author

Emrehan Halici (emrehan(AT)halici.com.tr), Apr 24 2004

Extensions

Edited by Ralf Stephan, Apr 26 2004

Status

approved