A096958 Fifth column (m=4) of (1,6)-Pascal triangle A096956.

6, 25, 65, 135, 245, 406, 630, 930, 1320, 1815, 2431, 3185, 4095, 5180, 6460, 7956, 9690, 11685, 13965, 16555, 19481, 22770, 26450, 30550, 35100, 40131, 45675, 51765, 58435, 65720, 73656, 82280, 91630, 101745, 112665, 124431, 137085, 150670

Offset: 0

Author

Wolfdieter Lang, Aug 13 2004

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A000332, A096956.

Cf. other columns: A096957 (m = 3), A096959 (m = 5), A097297 (m = 6), A097298 (m = 7), A097299 (m = 8), A097300 (m = 9).

Programs

Magma

[(n+24)*Binomial(n+3, 3) div 4: n in [0..40]]; // Vincenzo Librandi, Oct 01 2013

Mathematica

Table[(n + 24) Binomial[n+3, 3]/4, {n, 0, 50}] (* Vincenzo Librandi, Oct 01 2013 *)

Formula

a(n) = A096956(n+4, 4) = 6*b(n) - 5*b(n-1) = (n+24)*binomial(n+3, 3)/4, with b(n) = A000332(n) = binomial(n+4, 4).

G.f.: (6-5*x)/(1-x)^5.

a(n) = sum_{k=1..n+1} ( sum_{i=1..k} i*(n-k+7) ). - Wesley Ivan Hurt, Sep 26 2013