OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1653
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
KEYWORD
nonn
AUTHOR
Peter Luschny, Jan 26 2019
STATUS
approved