A104678 a(n) = binomial(n+4,4) * binomial(n+9,4).

126, 1050, 4950, 17325, 50050, 126126, 286650, 600600, 1178100, 2187900, 3879876, 6613425, 10892700, 17409700, 27096300, 41186376, 61289250, 89475750, 128378250, 181306125, 252378126, 346673250, 470401750, 631098000, 837837000, 1101476376, 1434925800

Offset

0,1

Links

Table of n, a(n) for n=0..26.

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

From R. J. Mathar, Nov 29 2015: (Start)

a(n) = A000332(n+4)*A000332(n+9).

G.f.: ( -126+84*x-36*x^2+9*x^3-x^4 ) / (x-1)^9. (End)

From Amiram Eldar, Aug 30 2022: (Start)

Sum_{n>=0} 1/a(n) = 9/980.

Sum_{n>=0} (-1)^n/a(n) = 1/140. (End)

Example

If n=0 then C(0+4,0+0)*C(0+9,4) = C(4,0)*C(9,4) = 1*126 = 126.
If n=5 then C(5+4,5+0)*C(5+9,4) = C(9,5)*C(14,4) = 126*1001 = 126126.

Maple

A104678:=n->binomial(n+4, n)*binomial(n+9, 4); seq(A104678(n), n=0..100); # Wesley Ivan Hurt, Dec 03 2013

Mathematica

Table[Binomial[n + 4, n] Binomial[n + 9, 4], {n, 0, 100}] (* Wesley Ivan Hurt, Dec 03 2013 *)

Crossrefs

Cf. A000332, A062190.

Sequence in context: A342307 A151989 A318626 * A154093 A172139 A194717

Adjacent sequences: A104675 A104676 A104677 * A104679 A104680 A104681

Keyword

easy,nonn

Author

Zerinvary Lajos, Apr 22 2005

Status

approved