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15, 315, 1287, 3315, 6783, 12075, 19575, 29667, 42735, 59163, 79335, 103635, 132447, 166155, 205143, 249795, 300495, 357627, 421575, 492723, 571455, 658155, 753207, 856995, 969903, 1092315, 1224615, 1367187, 1520415, 1684683, 1860375, 2047875, 2247567, 2459835
Cf. A001539, A154633.
a(0)=15, a(1)=315, a(2)=1287, a(3)=3315; for n>3, a(n) = 4*a(n-1)-) - 6*a(n-2)+ ) + 4*a(n-3)- ) - a(n-4). - _) for n>3. - _Harvey P. Dale_, May 06 2012
L. B. W. Jolley, Summation of Series, Dover (, 1961)..
sum(4/((4*m+1)*(4*m+3)*(4*m+5)), m=0..infinity) = (Pi-2)/4. [Jolley eq 238]
Sum_{n>=0} 4/a(n) = (Pi-2)/4. [Jolley, eq. 238]
From _Sum_{n>=0} (-1)^n/a(n) = 1/8 + (log(2*sqrt(2)+3) - Pi)/(16*sqrt(2)). - _Amiram Eldar_, Feb 27 2022: (Start)
Sum_{n>=0} 1/a(n) = (Pi-2)/16.
Sum_{n>=0} (-1)^n/a(n) = 1/8 + (log(2*sqrt(2)+3) - Pi)/(16*sqrt(2)). (End)
From Amiram Eldar, Feb 27 2022: (Start)
a(0)=15, a(1)=315, a(2)=1287, a(3)=3315; for n>3, a(n) = 4*a(n-1)-6*a(n-2)+ 4*a(n-3)- a(n-4). [_). - _Harvey P. Dale_, May 06 2012]
(PARI) a(n)=(4*n+1)*(4*n+3)*(4*n+5) \\ Charles R Greathouse IV, Oct 16 2015