A018217 Sum(C(j)*(n-j)*4^(n-j),j=0..n-1), C = Catalan numbers.

0, 4, 36, 232, 1300, 6744, 33320, 159184, 742068, 3395320, 15308920, 68213424, 300999816, 1317415792, 5726300880, 24742452128, 106357582324, 455122855224, 1939780103768, 8238185701360, 34876073003352, 147223869286736, 619871651308336, 2603757232133472, 10913483674589000

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

Recurrence: (n-1)*n*a(n) = 2*(n-1)*(4*n+1)*a(n-1) - 8*n*(2*n-1)*a(n-2). - Vaclav Kotesovec, Oct 07 2012

G.f.: 2/(1-4*x)^2 - 2/(1-4*x)^(3/2). - Mark van Hoeij, Mar 28 2013

Mathematica

Table[2*(n+1)*(4^n-Binomial[2*n+1, n]), {n, 0, 20}] (* Vaclav Kotesovec, Oct 07 2012 *)
Table[Sum[CatalanNumber[j](n-j)4^(n-j), {j, 0, n-1}], {n, 0, 30}] (* Harvey P. Dale, Jul 17 2023 *)

Prog

(PARI) x='x+O('x^66); concat([0], Vec( 2/(1-4*x)^2 - 2/(1-4*x)^(3/2) ) ) \\ Joerg Arndt, May 04 2013

Crossrefs

Sequence in context: A257888 A197424 A306094 * A003488 A295411 A218516

Adjacent sequences: A018214 A018215 A018216 * A018218 A018219 A018220

Keyword

nonn,easy

Author

N. J. A. Sloane, Peter Winkler (pw(AT)bell-labs.com)

Status

approved