A096959 Sixth column (m=5) of (1,6)-Pascal triangle A096956.

6, 31, 96, 231, 476, 882, 1512, 2442, 3762, 5577, 8008, 11193, 15288, 20468, 26928, 34884, 44574, 56259, 70224, 86779, 106260, 129030, 155480, 186030, 221130, 261261, 306936, 358701, 417136, 482856, 556512, 638792, 730422, 832167, 944832

Offset: 0

Author

Wolfdieter Lang, Aug 13 2004

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A096958 (fifth column), A097297 (seventh column).

Programs

Magma

[(n+30)*Binomial(n+4, 4)/5: n in [0..30]]; // G. C. Greubel, Nov 24 2017

Mathematica

Table[(n + 30)*Binomial[n + 4, 4]/5, {n, 0, 50}] (* G. C. Greubel, Nov 24 2017 *)

PARI

for(n=0,30, print1((n+30)*binomial(n+4, 4)/5, ", ")) \\ G. C. Greubel, Nov 24 2017

Formula

a(n) = A096956(n+5, 5).

a(n) = 6*b(n) - 5*b(n-1), with b(n) = A000389(n+5) = binomial(n+5, 5).

a(n) = (n+30)*binomial(n+4, 4)/5.

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

E.g.f.: x*(720 + 1140*x + 420*x^2 + 45*x^3 + x^4)*exp(x)/120. - G. C. Greubel, Nov 24 2017