A131528 a(n) = (n^1 + 1!)*(n^2 + 2!)*(n^3 + 3!)*(n^4 + 4!)/2!.

144, 525, 5040, 76230, 882000, 6886539, 38974320, 172650300, 633845520, 2008589625, 5657204784, 14470043490, 34161950160, 75378387735, 156979350000, 310979592504, 589757174160, 1076298622245, 1898430030000, 3248190882750, 5407743199824, 8783474489955

Offset: 0

Author

Alexander R. Povolotsky, Aug 25 2007

Keywords

• nonn
• easy

Comments

The values of m = m(k) needed to make the sequence a(n,k) = m (n^1 + 1!) (n^2 + 2!) ... (n^k + k!) / k! (n >= 0) take integral values for all n are given in A049614. - Peter J. C. Moses, Aug 29 2007

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Crossrefs

Cf. A049614, A131683.

Programs

Mathematica

a[n_]:=(n+1)(n^2+2)(n^3+6)(n^4+24)/2;Table[a[n],{n,0,21}] (* or *) LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{144, 525, 5040, 76230, 882000, 6886539, 38974320, 172650300, 633845520, 2008589625,5657204784, 14470043490},22] (* James C. McMahon, Feb 25 2025 *)

Formula

G.f.: (-3*(48 + x*(-353 + x*(2395 + x*(8635 + x*(93855 + x*(217437 + x*(213873 + 5*x*(12325 + x*(1441 + 16*x)))))))))) / (x - 1)^11. - Peter J. C. Moses, Aug 29 2007

a(n) = 3*A131683(n). - James C. McMahon, Feb 26 2025