A387280 Expansion of 1/((1-2*x) * (1-6*x))^(5/2).
1, 20, 250, 2520, 22470, 185304, 1448580, 10895280, 79603590, 568642360, 3989693708, 27585223120, 188421602460, 1273887926640, 8537435428680, 56785445628768, 375214194393030, 2464893754074360, 16109413813808700, 104800627073105040, 678975482198143284, 4382524104695787600
Offset: 0
Links
- Paolo Xausa, Table of n, a(n) for n = 0..1000
Programs
-
Mathematica
Module[{x}, CoefficientList[Series[1/((3*x - 2)*4*x + 1)^(5/2), {x, 0, 25}], x]] (* Paolo Xausa, Aug 25 2025 *) -
PARI
my(N=30, x='x+O('x^N)); Vec(1/((1-2*x)*(1-6*x))^(5/2))
Formula
n*a(n) = (8*n+12)*a(n-1) - 12*(n+3)*a(n-2) for n > 1.
a(n) = (-2)^n * Sum_{k=0..n} 3^k * binomial(-5/2,k) * binomial(-5/2,n-k).
a(n) = 2^n * Sum_{k=0..n} (-2)^k * binomial(-5/2,k) * binomial(n+4,n-k).
a(n) = Sum_{k=0..n} 4^k * 6^(n-k) * binomial(-5/2,k) * binomial(n+4,n-k).
a(n) = (binomial(n+4,2)/6) * A387272(n).
a(n) = (-1)^n * Sum_{k=0..n} 8^k * (3/2)^(n-k) * binomial(-5/2,k) * binomial(k,n-k).