A104475 a(n) = binomial(n+4,4) * binomial(n+8,4).
70, 630, 3150, 11550, 34650, 90090, 210210, 450450, 900900, 1701700, 3063060, 5290740, 8817900, 14244300, 22383900, 34321980, 51482970, 75710250, 109359250, 155405250, 217567350, 300450150, 409704750, 552210750, 736281000, 971890920, 1270934280, 1647507400, 2118223800
Offset: 0
Examples
a(0): C(0+4,4)*C(0+8,4) = C(4,4)*C(8,4) = 1*70 = 70. a(7): C(5+4,4)*C(5+8,4) = C(9,4)*(13,4) = 126*715 = 90090.
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
Programs
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Magma
[Binomial(n+4,4)*Binomial(n+8,4): n in [0..30]]; // Vincenzo Librandi, Jul 31 2015
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Maple
A104475:=n->binomial(n+4,4)*binomial(n+8,4): seq(A104475(n), n=0..40); # Wesley Ivan Hurt, Jan 29 2017
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Mathematica
f[n_] := Binomial[n + 4, 4]Binomial[n + 8, 4]; Table[ f[n], {n, 0, 25}] (* Robert G. Wilson v, Apr 20 2005 *) -
PARI
vector(30, n, n--; binomial(n+4,4)*binomial(n+8,4)) \\ Michel Marcus, Jul 31 2015
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SageMath
def A104475(n): return binomial(n+4,4)*binomial(n+8,4) print([A104475(n) for n in range(31)]) # G. C. Greubel, Mar 05 2025
Formula
a(n) = 70*A000581(n-8). - Michel Marcus, Jul 31 2015
From Amiram Eldar, Aug 30 2022: (Start)
Sum_{n>=0} 1/a(n) = 4/245.
Sum_{n>=0} (-1)^n/a(n) = 512*log(2)/35 - 37216/3675. (End)
From G. C. Greubel, Mar 05 2025: (Start)
G.f.: 70/(1-x)^9.
E.g.f.: (1/576)*(40320 + 322560*x + 564480*x^2 + 376320*x^3 + 117600*x^4 + 18816*x^5 + 1568*x^6 + 64*x^7 + x^8)*exp(x). (End)
Extensions
More terms from Robert G. Wilson v, Apr 20 2005