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A096959 Sixth column (m=5) of (1,6)-Pascal triangle A096956. 3

%I

%S 6,31,96,231,476,882,1512,2442,3762,5577,8008,11193,15288,20468,26928,

%T 34884,44574,56259,70224,86779,106260,129030,155480,186030,221130,

%U 261261,306936,358701,417136,482856,556512,638792,730422,832167,944832

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

%H G. C. Greubel, <a href="/A096959/b096959.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

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

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

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

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

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

%t Table[(n + 30)*Binomial[n + 4, 4]/5, {n, 0, 50}] (* _G. C. Greubel_, Nov 24 2017 *)

%o (PARI) for(n=0,30, print1((n+30)*binomial(n+4, 4)/5, ", ")) \\ _G. C. Greubel_, Nov 24 2017

%o (MAGMA) [(n+30)*Binomial(n+4, 4)/5: n in [0..30]]; // _G. C. Greubel_, Nov 24 2017

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

%K nonn,easy

%O 0,1

%A _Wolfdieter Lang_, Aug 13 2004

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Last modified February 20 21:57 EST 2020. Contains 332084 sequences. (Running on oeis4.)