A383892 Expansion of 1/( ((1-x)*(1-2*x)*(1-3*x)*(1-4*x))^2 * (1-5*x) ).
1, 25, 355, 3775, 33502, 262570, 1880090, 12574850, 79778303, 485441135, 2856558005, 16358449625, 91615095204, 503740623720, 2727832278900, 14584759018500, 77152991893005, 404503014170325, 2104862289863575, 10883633564375875, 55976319375728506, 286601257317512950
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..500
- Index entries for linear recurrences with constant coefficients, signature (25,-270,1650,-6273,15345,-24080,23300,-12576,2880).
Programs
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Magma
[1] cat [&+[StirlingSecond(k+4,4) * StirlingSecond(n-k+5,5): k in [0..n]]: n in [1..25]]; // Vincenzo Librandi, May 23 2025
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Mathematica
a[n_]:=Sum [StirlingS2[k+4,4]*StirlingS2[n-k+5,5],{k,0,n}];Table[a[n],{n,0,19}] (* Vincenzo Librandi, May 23 2025 *) -
PARI
a(n) = sum(k=0, n, stirling(k+4, 4, 2)*stirling(n-k+5, 5, 2));
Formula
a(n) = 25*a(n-1) - 270*a(n-2) + 1650*a(n-3) - 6273*a(n-4) + 15345*a(n-5) - 24080*a(n-6) + 23300*a(n-7) - 12576*a(n-8) + 2880*a(n-9).
a(n) = Sum_{k=0..n} Stirling2(k+4,4) * Stirling2(n-k+5,5).