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Search: id:A083420
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| 1, 7, 31, 127, 511, 2047, 8191, 32767, 131071, 524287, 2097151, 8388607, 33554431, 134217727, 536870911, 2147483647, 8589934591, 34359738367, 137438953471, 549755813887, 2199023255551, 8796093022207, 35184372088831
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Sum of divisors of 4^n. - Paul Barry (pbarry(AT)wit.ie), Oct 13 2005
a(n) = A099393(n) + A020522(n) = A000302(n) + A024036(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Feb 07 2006
Subsequence of A000069; A132680(a(n)) = A005408(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 26 2007
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LINKS
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Eric Weisstein's World of Mathematics, Rule 220
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FORMULA
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G.f. (1+2x)/((1-x)(1-4x)) E.g.f. 2exp(4x)-exp(x)
With a leading zero, this is a(n)=(4^n-2+0^n)/2, the binomial transform of A080925. - Paul Barry (pbarry(AT)wit.ie), May 19 2003
a(n) = (-16^n/2)*B(2n, 1/4)/B(2n) where B(n, x) is the n-th Bernoulli polynomial and B(k)=B(k, 0) is the k-th Bernoulli number. a(n)=5*a(n-1)-4*a(n-2). Also a(n) = (-4^n/2)*B(2n, 1/2)/B(2n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 18 2004
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MAPLE
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[seq (stirling2(2*n, 2), n=1..23)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 06 2006
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CROSSREFS
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Cf. A083421.
Sequence in context: A036280 A056909 A002147 this_sequence A036282 A033474 A001896
Adjacent sequences: A083417 A083418 A083419 this_sequence A083421 A083422 A083423
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Apr 29 2003
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