A306185
a(n) = (2n+1)!! + (2n)!! where k!! = A006882(k).
Original entry on oeis.org
5, 23, 153, 1329, 14235, 181215, 2672145, 44781345, 840523635, 17465201775, 397983749625, 9867844134225, 264469801070475, 7618612476650175, 234748657653134625, 7703855828862818625, 268263758052098683875, 9879138385352252391375, 383608053176023482431625, 15664153113813817068080625
Offset: 1
a(3) = A006882(7) + A006882(6) = (7*5*3) + (6*4*2) = 105 + 48 = 153.
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o=e=1
for n in range(2, 99, 2):
o*=n+1
e*=n
print(o+e, end=', ')
A263384
Fourth column of the matrix of polynomial coefficients of the rational approximation to Mill's ratio.
Original entry on oeis.org
1, 14, 185, 2640, 41685, 729330, 14073885, 297693900, 6859400625, 171172905750, 4601737965825, 132643472761800, 4082080279402125, 133614981594344250, 4635763624512145125, 169957871025837394500
Offset: 0
- Selden Crary, Richard Diehl Martinez, Michael Saunders, The Nu Class of Low-Degree-Truncated Rational Multifunctions. Ib. Integrals of Matern-correlation functions for all odd-half-integer class parameters, arXiv:1707.00705 [stat.ME], 2017, Table 2.
- A. Kreinin, Combinatorial properties of the Mills Ratio, arXiv:1405.5852 [math.CO], 2014.
- Alexander Kreinin, Integer Sequences Connected to the Laplace Continued Fraction and Ramanujan's Identity, Journal of Integer Sequences, 19 (2016), #16.6.2.
Columns of the matrix [q_{k,m}] include:
A000165 (m=1),
A129890 (m=2),
A035101 (m=3), this sequence (m=4).
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Table[((2 n + 6)!! - 3 (2 n + 5)!! + (2 n + 3)!!)/6, {n, 0, 12}] (* Michael De Vlieger, Oct 27 2015 *)
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a(n)=(prod(k=1, n+3, 2*k)-3*prod(k=1, n+3,(2*k-1))+prod(k=1, n+2, 2*k-1))/6;
vector(20, n, a(n-1)) \\ Altug Alkan, Oct 16 2015
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