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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This is the fifth member of the family A000079 (powers of 2), A016129, A016309, A071952, etc.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..500

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

Cf. A089278, A089500.

Sequence in context: A069296 A349466 A075923 * A266739 A227273 A298463

Adjacent sequences:  A089271 A089272 A089273 * A089275 A089276 A089277

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Nov 07 2003

STATUS

approved

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Last modified August 9 12:05 EDT 2022. Contains 356026 sequences. (Running on oeis4.)