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A053369 Linear recursion with Catalan numbers. 1
2, 9, 32, 115, 420, 1554, 5808, 21879, 82940, 316030, 1209312, 4644094, 17889032, 69089700, 267444000, 1037348415, 4030774380, 15687019590, 61137753600, 238580530650, 932105099640, 3645473785980, 14271279927840, 55918717024950, 219283705045080, 860564513057004, 3379592965275968 (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

a(n) = (7n+2)*C(n) where C(n)=Catalan numbers (A000108).

MATHEMATICA

Table[(7*n + 2)*CatalanNumber[n], {n, 0, 50}] (* G. C. Greubel, May 25 2018 *)

PROG

(PARI) for(n=0, 30, print1(((7*n+2)/(n+1))*binomial(2*n, n), ", ")) \\ G. C. Greubel, May 25 2018

(MAGMA) [((7*n+2)/(n+1))*Binomial(2*n, n): n in [0..30]]; // G. C. Greubel, May 25 2018

CROSSREFS

Cf. A050960.

Sequence in context: A053152 A077644 A292482 * A076959 A003697 A006253

Adjacent sequences:  A053366 A053367 A053368 * A053370 A053371 A053372

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 November 21 22:35 EST 2019. Contains 329383 sequences. (Running on oeis4.)