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

%I A096958 #21 May 02 2025 10:30:30
%S A096958 6,25,65,135,245,406,630,930,1320,1815,2431,3185,4095,5180,6460,7956,
%T A096958 9690,11685,13965,16555,19481,22770,26450,30550,35100,40131,45675,
%U A096958 51765,58435,65720,73656,82280,91630,101745,112665,124431,137085,150670
%N A096958 Fifth column (m=4) of (1,6)-Pascal triangle A096956.
%H A096958 Vincenzo Librandi, <a href="/A096958/b096958.txt">Table of n, a(n) for n = 0..1000</a>
%H A096958 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A096958 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).
%F A096958 G.f.: (6-5*x)/(1-x)^5.
%F A096958 a(n) = sum_{k=1..n+1} ( sum_{i=1..k} i*(n-k+7) ). - _Wesley Ivan Hurt_, Sep 26 2013
%t A096958 Table[(n + 24) Binomial[n+3, 3]/4, {n, 0, 50}] (* _Vincenzo Librandi_, Oct 01 2013 *)
%o A096958 (Magma) [(n+24)*Binomial(n+3, 3) div 4: n in [0..40]]; // _Vincenzo Librandi_, Oct 01 2013
%Y A096958 Cf. A000332, A096956.
%Y A096958 Cf. other columns: A096957 (m = 3), A096959 (m = 5), A097297 (m = 6), A097298 (m = 7), A097299 (m = 8), A097300 (m = 9).
%K A096958 nonn,easy
%O A096958 0,1
%A A096958 _Wolfdieter Lang_, Aug 13 2004