A209359 a(n) = 2^n * (n^4 - 4*n^3 + 18*n^2 - 52*n + 75) - 75.

0, 1, 33, 357, 2405, 12405, 53877, 207541, 731829, 2411445, 7531445, 22523829, 64991157, 181977013, 496680885, 1326120885, 3473604533, 8947236789, 22706651061, 56869519285, 140755599285, 344683708341, 835954147253, 2009692372917, 4792831180725, 11346431180725

Offset: 0

Author

Bruno Berselli, Mar 07 2012

Keywords

• nonn
• easy

Comments

This sequence is related to A036828 by the transform a(n) = n*A036828(n) - sum(A036828(i), i=0..n-1).

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• B. Berselli, A description of the transform in Comments lines: website Matem@ticamente (in Italian).
• Index entries for linear recurrences with constant coefficients, signature (11,-50,120,-160,112,-32).

Crossrefs

Cf. A000079, A000337, A036826, A036828.

Programs

Magma

m:=25; R:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!((1+2*x)*(1+20*x+4*x^2)/((1-x)*(1-2*x)^5)));

Mathematica

LinearRecurrence[{11, -50, 120, -160, 112, -32}, {0, 1, 33, 357, 2405, 12405}, 26]
Table[2^n(n^4-4n^3+18n^2-52n+75)-75,{n,0,30}] (* Harvey P. Dale, Mar 08 2023 *)

PARI

for(n=0, 25, print1(2^n*(n^4-4*n^3+18*n^2-52*n+75)-75", "));

Formula

G.f.: x*(1+2*x)*(1+20*x+4*x^2)/((1-x)*(1-2*x)^5).

a(n) = (1/2) * Sum_{k=0..n} Sum_{i=0..n} k^4 * C(k,i). - Wesley Ivan Hurt, Sep 21 2017