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A089274
Fifth column of the Legendre-Stirling triangle A071951.
3
1, 70, 3192, 121424, 4203824, 137922336, 4380918784, 136378114048, 4191383868672, 127754693361152, 3873052857829376, 117001609550671872, 3526270158211870720, 106112798944292282368, 3189880933574260359168
OFFSET
0,2
COMMENTS
This is the fifth member of the family A000079 (powers of 2), A016129, A016309, A071952, etc.
LINKS
Index entries for linear recurrences with constant coefficients, signature (70, -1708, 17544, -72000, 86400).
FORMULA
G.f.: 1/((1-2*1*x)*(1-3*2*x)*(1-4*3*x)*(1-5*4*x)*(1-6*5*x)).
a(n) = (16875*(6*5)^n -20000*(5*4)^n +6048*(4*3)^n -405*(3*2)^n +2*(2*1)^n)/2520.
a(n) = A071951(n+5, 5), n>=0.
a(n) = det(|ps(i+5,j+4)|, 1 <= i,j <= n), where ps(n,k) are Legendre-Stirling numbers of the first kind (A129467). [Mircea Merca, Apr 06 2013]
PROG
(Magma) [(16875*(6*5)^n - 20000*(5*4)^n + 6048*(4*3)^n - 405*(3*2)^n + 2*(2*1)^n)/2520: n in [0..20]]; // Vincenzo Librandi, Sep 02 2011
CROSSREFS
Sequence in context: A069296 A349466 A075923 * A266739 A227273 A298463
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Nov 07 2003
STATUS
approved