A105252 a(n) = binomial(n+5,n)*binomial(n+9,n).

1, 60, 1155, 12320, 90090, 504504, 2312310, 9060480, 31286970, 97337240, 277411134, 733649280, 1818838840, 4261894560, 9502285320, 20271542016, 41572498275, 82281899700, 157706974425, 293570877600, 532097215650, 941124327000, 1627522854750, 2756636064000

Offset

0,2

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).

Formula

G.f.: (1+45*x+360*x^2+840*x^3+630*x^4+126*x^5)/(1-x)^15. - Colin Barker, Jan 21 2013

From Amiram Eldar, Sep 01 2022: (Start)

Sum_{n>=0} 1/a(n) = 7425*Pi^2/2 - 114902691/3136.

Sum_{n>=0} (-1)^n/a(n) = 28960047/15680 - 255*Pi^2/4 - 12288*log(2)/7. (End)

Example

a(0): C(0+5,0)*C(0+9,0) = C(5,0)*C(9,0) = 1*1 = 1;
a(10): C(10+5,10)*C(10+9,10) = C(15,10)*(19,10) = 3003*92378 = 277411134.

Mathematica

f[n_] := Binomial[n + 5, n]Binomial[n + 9, n]; Table[ f[n], {n, 0, 20}] (* Robert G. Wilson v, Apr 20 2005 *)

Prog

(Magma) [Binomial(n+5, n)*Binomial(n+9, n): n in [0..30]]; // Vincenzo Librandi, Jul 31 2015
(Python)
A105252_list, m = [], [2002, -4433, 3487, -1133, 127, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
for _ in range(10**2):
    A105252_list.append(m[-1])
    for i in range(14):
        m[i+1] += m[i] # Chai Wah Wu, Dec 15 2015
(SageMath)
def A105252(n): return binomial(n+5, n)*binomial(n+9, n)
print([A105252(n) for n in range(31)]) # G. C. Greubel, Mar 04 2025

Crossrefs

Cf. A062264.

Sequence in context: A056352 A056346 A283722 * A269138 A146347 A289156

Adjacent sequences: A105249 A105250 A105251 * A105253 A105254 A105255

Keyword

easy,nonn

Author

Zerinvary Lajos, Apr 14 2005

Extensions

More terms from Robert G. Wilson v, Apr 20 2005

Status

approved