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A053368 a(n) = (5n+2)*C(n) where C(n)=Catalan numbers (A000108). 1
2, 7, 24, 85, 308, 1134, 4224, 15873, 60060, 228514, 873392, 3350802, 12896744, 49774300, 192559680, 746503065, 2899328940, 11279096730, 43942760400, 171424529430, 669540282840, 2617890571140, 10246047127680, 40137974797050, 157368305973528, 617467192984404, 2424490605524064 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

3*(n+1)*a(n) + 2*(-7*n-2)*a(n-1) + 4*(2*n-3)*a(n-2) = 0. - R. J. Mathar, Feb 13 2015

-(n+1)*(5*n-3)*a(n) + 2*(5*n+2)*(2*n-1)*a(n-1) = 0. - R. J. Mathar, Feb 13 2015

MATHEMATICA

Table[(5*n + 2)*CatalanNumber[n], {n, 0, 50}] (* G. C. Greubel, May 25 2018 *)

PROG

(PARI) for(n=0, 30, print1(((5*n+2)/(n+1))*binomial(2*n, n), ", ")) \\ G. C. Greubel, May 25 2018

(MAGMA) [((5*n+2)/(n+1))*Binomial(2*n, n): n in [0..30]]; // G. C. Greubel, May 25 2018

CROSSREFS

Cf. A050960.

Sequence in context: A144170 A297345 A052986 * A141753 A014300 A128086

Adjacent sequences:  A053365 A053366 A053367 * A053369 A053370 A053371

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, Jan 06 2000

EXTENSIONS

Terms a(21) onward added by G. C. Greubel, May 25 2018

STATUS

approved

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Last modified April 19 06:30 EDT 2019. Contains 322237 sequences. (Running on oeis4.)