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A076036 G.f.: 1/(1 - 5*x*C(x)), where C(x) = (1 - sqrt(1 - 4*x))/(2*x) = g.f. for the Catalan numbers A000108. 11
1, 5, 30, 185, 1150, 7170, 44760, 279585, 1746870, 10916150, 68219860, 426353130, 2664633580, 16653699860, 104084695500, 650526003825, 4065775405350, 25411052086350, 158818913483700, 992617612224750, 6203857867325700, 38774103465635100, 242338116077385600 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Numbers have the same parity as the Catalan numbers, that is, a(n) is even except for n of the form 2^m - 1. Follows from C(x) = 1/(1 - x*C(x)) = 1/(1 - 5*x*C(x)) (mod 2). - Peter Bala, Jul 24 2016

LINKS

Table of n, a(n) for n=0..22.

FORMULA

a(n) = Sum_{k = 0..n} A106566(n, k)*5^k . - Philippe Deléham, Sep 01 2005

a(n) = Sum{k = 0..n} A039599(n,k)*4^k. - Philippe Deléham, Sep 08 2007

a(0) = 1, a(n) = (25*a(n-1) - 5*A000108(n-1))/4 for n >= 1 . - Philippe Deléham, Nov 27 2007

a(n) = Sum_{k = 0..n} A116395(n,k)*3^k. [Philippe Deléham, Sep 27 2009]

CROSSREFS

Cf. A000108, A000984, A007854, A076035, A126694.

Sequence in context: A227383 A155195 A147837 * A195257 A161407 A006773

Adjacent sequences:  A076033 A076034 A076035 * A076037 A076038 A076039

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Oct 29 2002

STATUS

approved

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Last modified February 17 16:26 EST 2018. Contains 299296 sequences. (Running on oeis4.)