A383893 Expansion of 1/( ((1-x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-5*x))^2 * (1-6*x) ).

1, 36, 721, 10626, 128758, 1360128, 12978758, 114537348, 950326391, 7502910996, 56878787231, 416937779286, 2971567050420, 20682844799760, 141092113563660, 946112664225960, 6251628891468765, 40789040893547940, 263235445374827965, 1682802305881045290, 10669738322822387746

Offset: 0

Author

Seiichi Manyama, May 14 2025

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (36,-575,5370,-32523,133848,-381065,748530,-991276,840216,-408960,86400).

Crossrefs

Column k=6 of A287532.

Programs

Magma

[1] cat [&+[StirlingSecond(k+5,5) * StirlingSecond(n-k+6,6): k in [0..n]]: n in [1..25]]; // Vincenzo Librandi, May 23 2025

Mathematica

a[n_]:=Sum [StirlingS2[k+5,5]*StirlingS2[n-k+6,6],{k,0,n}];Table[a[n],{n,0,19}] (* Vincenzo Librandi, May 23 2025 *)

PARI

a(n) = sum(k=0, n, stirling(k+5, 5, 2)*stirling(n-k+6, 6, 2));

Formula

a(n) = 36*a(n-1) - 575*a(n-2) + 5370*a(n-3) - 32523*a(n-4) + 133848*a(n-5) - 381065*a(n-6) + 748530*a(n-7) - 991276*a(n-8) + 840216*a(n-9) - 408960*a(n-10) + 86400*a(n-11).

a(n) = Sum_{k=0..n} Stirling2(k+5,5) * Stirling2(n-k+6,6).