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A096958 Fifth column (m=4) of (1,6)-Pascal triangle A096956. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

MAPLE

seq(sum(sum(i*(j-k+7), i=1..k), k=1..j+1), j=0..100); # Wesley Ivan Hurt, Sep 26 2013

MATHEMATICA

s1=s2=s3=s4=0; lst={}; Do[a=n+(n+2); s1+=a; s2+=s1; s3+=s2; s4+=s3; AppendTo[lst, s3/2], {n, 5, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Apr 04 2009 *)

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. A096957 (fourth column), A096959 (sixth column).

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

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Last modified February 23 00:28 EST 2020. Contains 332157 sequences. (Running on oeis4.)