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

0,2

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).

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).

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 *)

Prog

(PARI) a(n) = sum(k=0, n, stirling(k+4, 4, 2)*stirling(n-k+5, 5, 2));
(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

Crossrefs

Column k=5 of A287532.

Cf. A383842.

Sequence in context: A282924 A022653 A125460 * A188487 A306083 A392723

Adjacent sequences: A383889 A383890 A383891 * A383893 A383894 A383895

Keyword

nonn,easy

Author

Seiichi Manyama, May 14 2025

Status

approved