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

Author

Barry E. Williams, Jan 06 2000

Keywords

• easy
• nonn

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

Crossrefs

Cf. A050960.

Programs

Magma

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

Mathematica

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

PARI

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

Formula

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

Extensions

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