A045889 Partial sums of A045618.

1, 7, 30, 102, 303, 825, 2116, 5200, 12381, 28779, 65658, 147594, 327835, 721069, 1573056, 3408084, 7340265, 15728895, 33554710, 71303470, 150995271, 318767457, 671089020, 1409286552, 2952790453, 6174015955, 12884902386

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Crossrefs

Cf. A045618.

Programs

Mathematica

Table[(n^2 + 11 n + 34)/2 + (n - 2)*2^(n + 3), {n, 0, 26}] (* or *)
CoefficientList[Series[1/((1 - 2 x)^2*(1 - x)^3), {x, 0, 26}], x] (* Michael De Vlieger, Sep 21 2017 *)

PARI

Vec(1/((1-2*x)^2*(1-x)^3) + O(x^40)) \\ Michel Marcus, Sep 20 2017

Formula

a(n) = (n^2+11*n+34)/2 + (n-2)*2^(n+3).

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

a(n) = Sum_{k=1..n+4} Sum_{i=1..n+4} (i-k) * C(n-k+4,i). - Wesley Ivan Hurt, Sep 19 2017