A069975 a(n) = n*(16*n^2 - 1).
15, 126, 429, 1020, 1995, 3450, 5481, 8184, 11655, 15990, 21285, 27636, 35139, 43890, 53985, 65520, 78591, 93294, 109725, 127980, 148155, 170346, 194649, 221160, 249975, 281190, 314901, 351204, 390195, 431970, 476625, 524256, 574959, 628830, 685965, 746460
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Mathematica
Table[n(16n^2-1),{n,40}] (* Harvey P. Dale, Dec 17 2018 *) -
PARI
a(n) = n*(16*n^2-1); \\ Michel Marcus, Nov 25 2013
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PARI
my(x='x+O('x^37)); Vec(3*x*(5+22*x+5*x^2)/(1-x)^4) \\ Elmo R. Oliveira, Sep 05 2025
Formula
Sum_{n>=1} 1/a(n) = 3*log(2) - 2 = A016631 - 2. (Ramanujan)
Sum_{n>=1} (-1)^(n+1)/a(n) = 2 - log(2) + sqrt(2)*log(sqrt(2)-1). - Amiram Eldar, Jun 24 2022
From Elmo R. Oliveira, Sep 05 2025: (Start)
G.f.: 3*x*(5 + 22*x + 5*x^2)/(x-1)^4.
E.g.f.: x*(15 + 48*x + 16*x^2)*exp(x).
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4.
a(n) = A069140(n)/4. (End)
Extensions
More terms from Elmo R. Oliveira, Sep 05 2025