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A018217 Sum(C(j)*(n-j)*4^(n-j),j=0..n-1), C = Catalan numbers. 1
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 (list; graph; refs; listen; history; text; internal format)
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 *)

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: A074434 A257888 A197424 * 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

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Last modified February 22 19:36 EST 2018. Contains 299469 sequences. (Running on oeis4.)