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Search: id:A117202
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| A117202 |
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Binomial transform of n*F(n). |
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+0
3
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| 0, 1, 4, 15, 52, 170, 534, 1631, 4880, 14373, 41810, 120406, 343884, 975325, 2749852, 7713435, 21540304, 59917826, 166094370, 458998523, 1264919720, 3477182961, 9536877614, 26102772910, 71309161752, 194468551225, 529490287924
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Binomial transform of A045925.
Number of acyclic subgraphs of the wheel graph W_n (on n+1 vertices) with exactly n-1 edges. - E. R. Vaughan (e.vaughan(AT)qmul.ac.uk), Jun 12 2007
Starting (1, 4, 15, 52,...) = binomial transform of A136376: (1, 3, 8, 18, 37,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 03 2008]
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FORMULA
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G.f.: x(1-2x+2x^2)/(1-3x+x^2)^2; a(n)=6a(n-1)-11a(n-2)+6a(n-3)-a(n-4); a(n)=sum{k=0..n, C(n,k)*k*F(k)}.
a(n)=sum(k=1,n,F(2k)*B(2n-2k)*binomial(2n,2k)) where F=Fibonacci's numbers and B=Bernoulli's numbers ; a(n)=n*F(2n-1) - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 29 2006
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CROSSREFS
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Cf. A001519, A111262.
A136376 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 03 2008]
Sequence in context: A107307 A005492 A003013 this_sequence A137213 A027853 A132894
Adjacent sequences: A117199 A117200 A117201 this_sequence A117203 A117204 A117205
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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), Mar 02 2006
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