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Search: id:A091030
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| 1, 14, 183, 2380, 30941, 402234, 5229043, 67977560, 883708281, 11488207654, 149346699503, 1941507093540, 25239592216021, 328114698808274, 4265491084507563, 55451384098598320, 720867993281778161
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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13^a(n) is highest power of 13 dividing (13^n)!.
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FORMULA
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a(n)= sum(13^k, k=0..n-1) = (13^n-1)/12.
G.f.: x/((1-13*x)*(1-x))= (1/(1-13*x) - 1/(1-x))/12.
For analogues with primes 2, 3, 5, 7 and 11 see A000225, A003462, A003463, A023000 and A016123 respectively.
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MAPLE
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a:=n->sum(13^(n-j), j=1..n): seq(a(n), n=1..17); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 04 2007
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PROGRAM
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(Other) sage: [gaussian_binomial(n, 1, 13) for n in xrange(1, 18)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 28 2009]
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CROSSREFS
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Cf. A000225, A003462, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125.
Sequence in context: A163416 A097828 A030008 this_sequence A165152 A055759 A086946
Adjacent sequences: A091027 A091028 A091029 this_sequence A091031 A091032 A091033
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Jan 23 2004
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