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A323223 a(n) = [x^n] x/((1 - x)*(1 - 4*x)^(5/2)). 2
0, 1, 11, 81, 501, 2811, 14823, 74883, 366603, 1752273, 8218733, 37964449, 173172249, 781607349, 3496163949, 15517771749, 68412846069, 299828796219, 1307168814519, 5672308893819, 24511334499219, 105519144602439, 452695473616239, 1936085243038839, 8256615564926439 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = ((5*n + 1)*a(n-1) - (4*n + 2)*a(n-2))/(n - 1) for n >= 2.
a(n) = -(-4)^n*binomial(-5/2, n)*hypergeom([1, n+5/2], [n+1], 4) - i*sqrt(3)/27.
a(n) ~ 2^(2*n+2) * n^(3/2) / (9*sqrt(Pi)). - Vaclav Kotesovec, Jan 29 2019
a(n+1) - a(n) = A002802(n). - Seiichi Manyama, Jan 29 2019
MAPLE
A323223List := proc(len) local ogf, ser; ogf := (1 - 4*x)^(-5/2)*x/(1 - x);
ser := series(ogf, x, (n+1)*len+1); seq(coeff(ser, x, j), j=0..len) end:
A323223List(24);
# Alternative:
a := proc(n) option remember; `if`(n<2, n, ((5*n+1)*a(n-1)-(4*n+2)*a(n-2))/(n-1)) end: seq(a(n), n=0..24);
CROSSREFS
Row 5 of A323222.
Cf. A002802.
Sequence in context: A305826 A252817 A210064 * A211557 A333061 A055429
KEYWORD
nonn
AUTHOR
Peter Luschny, Jan 26 2019
STATUS
approved

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Last modified June 13 15:51 EDT 2024. Contains 373389 sequences. (Running on oeis4.)