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A107420
a(n) = C(n+5,5)*C(n+8,8).
1
1, 54, 945, 9240, 62370, 324324, 1387386, 5096520, 16563690, 48668620, 131405274, 330142176, 779502360, 1743502320, 3718285560, 7601828256, 14966099379, 28482196050, 52568991475, 94362067800, 165133618650, 282337298100, 472506635250, 775303893000, 1249100716500
OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).
FORMULA
From Chai Wah Wu, Apr 10 2021: (Start)
a(n) = 14*a(n-1) - 91*a(n-2) + 364*a(n-3) - 1001*a(n-4) + 2002*a(n-5) - 3003*a(n-6) + 3432*a(n-7) - 3003*a(n-8) + 2002*a(n-9) - 1001*a(n-10) + 364*a(n-11) - 91*a(n-12) + 14*a(n-13) - a(n-14) for n > 13.
G.f.: (56*x^5 + 350*x^4 + 560*x^3 + 280*x^2 + 40*x + 1)/(x - 1)^14. (End)
From Amiram Eldar, Sep 06 2022: (Start)
Sum_{n>=0} 1/a(n) = 2200*Pi^2 - 19150081/882.
Sum_{n>=0} (-1)^n/a(n) = 693421/490 - 20*Pi^2 - 12288*log(2)/7. (End)
EXAMPLE
a(0) = C(0+5,5)*C(0+8,8) = C(5,5)*C(8,8) = 1*1 = 1.
a(9) = C(9+5,5)*C(9+8,8) = C(14,5)*C(17,8) = 2002*24310 = 48668620.
MATHEMATICA
a[n_] := Binomial[n + 5, 5] * Binomial[n + 8, 8]; Array[a, 30, 0] (* Amiram Eldar, Sep 06 2022 *)
PROG
(PARI) for(n=0, 29, print1(binomial(n+5, 5)*binomial(n+8, 8), ", "))
CROSSREFS
Cf. A062145.
Sequence in context: A008401 A247048 A280479 * A298069 A281776 A160345
KEYWORD
easy,nonn
AUTHOR
Zerinvary Lajos, May 26 2005
EXTENSIONS
More terms from Rick L. Shepherd, May 27 2005
STATUS
approved