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

Author

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

Keywords

• easy
• nonn

Links

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

Crossrefs

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

Cf. A271476.

Programs

Mathematica

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

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

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

Extensions

Edited by Ralf Stephan, Apr 26 2004