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A378804
a(n) = n * 2^n * binomial(4*n, n).
2
0, 8, 224, 5280, 116480, 2480640, 51684864, 1060899840, 21541478400, 433812234240, 8680043806720, 172774871965696, 3424347806171136, 67626404043161600, 1331466198928588800, 26145958720005734400, 512257621575157678080, 10016204637370583089152, 195501127311163895316480
OFFSET
0,2
LINKS
Jonathan M. Borwein and Roland Girgensohn, Evaluations of binomial series, aequationes mathematicae, Vol. 70, No. 1 (2005), pp. 25-36.
FORMULA
a(n) = A036289(n) * A005810(n).
a(n) = 2^n * A378802(n).
a(n) == 0 (mod 8).
Sum_{n>=1} (-1)^n/a(n) = (log(2) - 6*log(3))/7 + Sum_{r: 2*r^3 + 12*r + 13 = 0} log(r+2)/(r+3) = -0.120716907732393305... (Borwein and Girgensohn, 2005, p. 32, eq. (43)).
MATHEMATICA
a[n_] := n * 2^n * Binomial[4*n, n]; Array[a, 20, 0]
PROG
(PARI) a(n) = n * 2^n * binomial(4*n, n);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Dec 07 2024
STATUS
approved