A107419 a(n) = C(n+4,4)*C(n+7,7).

1, 40, 540, 4200, 23100, 99792, 360360, 1132560, 3185325, 8179600, 19467448, 43439760, 91706160, 184497600, 355816800, 661028544, 1187785665, 2071432440, 3516320500, 5824819000, 9436206780, 14978106000, 23333661000, 35728290000, 53840548125, 79942445856

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 (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Formula

From Chai Wah Wu, Apr 10 2021: (Start)

a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12) for n > 11.

G.f.: (35*x^4 + 140*x^3 + 126*x^2 + 28*x + 1)/(x - 1)^12. (End)

From Amiram Eldar, Sep 06 2022: (Start)

Sum_{n>=0} 1/a(n) = 392*Pi^2 - 870268/225.

Sum_{n>=0} (-1)^n/a(n) = 56*Pi^2/3 - 3584*log(2)/15 - 441/25. (End)

Example

a(0) = C(0+4,4)*C(0+7,7) = C(4,4)*C(7,7) = 1*1 = 1.
a(6) = C(6+4,4)*C(6+7,7) = C(10,4)*C(13,7) = 210*1716 = 360360.

Mathematica

Table[Binomial[n+4, 4]Binomial[n+7, 7], {n, 0, 30}] (* Harvey P. Dale, Jul 27 2019 *)

Prog

(PARI) for(n=0, 29, print1(binomial(n+4, 4)*binomial(n+7, 7), ", "))

Crossrefs

Cf. A062145.

Sequence in context: A109105 A269692 A247409 * A159946 A185744 A269497

Adjacent sequences: A107416 A107417 A107418 * A107420 A107421 A107422

Keyword

easy,nonn

Author

Zerinvary Lajos, May 26 2005

Extensions

Corrected and extended by Rick L. Shepherd, May 27 2005

Status

approved