A053369 Linear recursion with Catalan numbers.

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

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