A383910 - OEIS

A383910

Expansion of Product_{k=0..3} (1 + k*x)/(1 - k*x).

1, 12, 72, 312, 1152, 3912, 12672, 39912, 123552, 378312, 1150272, 3481512, 10505952, 31640712, 95167872, 285995112, 858968352, 2578871112, 7740545472, 23229500712, 69704230752, 209144149512, 627495363072, 1882611918312, 5648087413152, 16944765555912, 50835303300672

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

Index entries for linear recurrences with constant coefficients, signature (6,-11,6).

FORMULA

a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n > 3.

a(n) = Sum_{k=0..3} |Stirling1(4,k+1)| * Stirling2(k+n,3).

a(n) = A383912(n) + 3*A383912(n-1) = 20*3^n - 15*2^(n+1) + 12 = 10*A091344(n) + 2 for n > 0.

PROG

(PARI) a(n) = if(n==0, 1, 20*3^n-15*2^(n+1)+12);