A316459 Expansion of 30*x*(1 + x) / (1 - x)^4.

30, 150, 420, 900, 1650, 2730, 4200, 6120, 8550, 11550, 15180, 19500, 24570, 30450, 37200, 44880, 53550, 63270, 74100, 86100, 99330, 113850, 129720, 147000, 165750, 186030, 207900, 231420, 256650, 283650, 312480, 343200, 375870, 410550, 447300, 486180

Offset: 1

Author

Colin Barker, Aug 12 2018

Keywords

• nonn
• easy

Comments

Seems to be the third column of A316349.

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A000330, A316349, A316457, A316458.

Programs

PARI

Vec(30*x*(1 + x) / (1 - x)^4 + O(x^40))

PARI

a(n) = 10*n^3 + 15*n^2 + 5*n

Formula

G.f.: 30*x*(1 + x) / (1 - x)^4.

a(n) = 30 * A000330(n).

a(n) = 10*n^3 + 15*n^2 + 5*n.

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