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

0,1

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).

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

From Amiram Eldar, Oct 26 2025: (Start)

Sum_{n>=0} 1/a(n) = 12759043123/52679663036.

Sum_{n>=0} (-1)^n/a(n) = 352*log(2)/161 - 3267227639321/2370584836620. (End)

Mathematica

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

Prog

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

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).

Sequence in context: A001664 A255687 A332698 * A166814 A241170 A245679

Adjacent sequences: A096955 A096956 A096957 * A096959 A096960 A096961

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 13 2004

Status

approved