A298371 a(n) = Sum_{m=0..n} Sum_{i=0..m} i*C(m-i,i)*C(m-i,n-m-i).

0, 0, 1, 3, 7, 17, 40, 90, 198, 430, 922, 1956, 4115, 8597, 17853, 36883, 75856, 155396, 317228, 645580, 1310132, 2652072, 5356277, 10795351, 21716195, 43608549, 87429944, 175025918, 349901074, 698604058, 1393149486, 2775103948, 5522129511, 10977608425

Offset: 0

Author

Vladimir Kruchinin, Jan 17 2018

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,1,0,-1,-4,-3,-2,-1).

Crossrefs

Cf. A000078.

Programs

Maxima

a(n):=sum(sum(i*binomial(m-i,i)*binomial(m-i,n-m-i),i,0,m),m,0,n);

PARI

concat(vector(2), Vec(x^2*(1 + x) / (1 - x - x^2 - x^3 - x^4)^2 + O(x^40))) \\ Colin Barker, Jan 18 2018

Formula

G.f.: x^3*(1 + x) / (1 - x - x^2 - x^3 - x^4)^2.

a(n) = 2*a(n-1) + a(n-2) - a(n-4) - 4*a(n-5) - 3*a(n-6) - 2*a(n-7) - a(n-8) for n>7. - Colin Barker, Jan 18 2018