A362126 Expansion of 1/(1 - x*(1+x)^2)^2.

1, 2, 7, 18, 47, 118, 290, 702, 1677, 3966, 9300, 21654, 50116, 115388, 264475, 603792, 1373621, 3115222, 7045205, 15892794, 35769390, 80337144, 180091131, 403002108, 900370600, 2008572044, 4474586920, 9955434456, 22123162421, 49107537598, 108891513251

Offset: 0

Author

Seiichi Manyama, Apr 08 2023

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (2,3,-2,-6,-4,-1).

Crossrefs

Column k=2 of A362125.

Cf. A002478, A362084.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(1/(1-x*(1+x)^2)^2)

Formula

a(n) = 2*a(n-1) + 3*a(n-2) - 2*a(n-3) - 6*a(n-4) - 4*a(n-5) - a(n-6) for n > 5.

a(n) = Sum_{k=0..n} (-1)^k * binomial(-2,k) * binomial(2*k,n-k) = Sum_{k=0..n} (k+1) * binomial(2*k,n-k).