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Search: id:A103210
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| A103210 |
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(1/n) * Sum[i=0..n-1, C(n,i)*C(n,i-1)*2^i*3^(n-i) ], a(0)=1. |
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15
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| 1, 3, 15, 93, 645, 4791, 37275, 299865, 2474025, 20819307, 178003815, 1541918901, 13503125805, 119352115551, 1063366539315, 9539785668657, 86104685123025, 781343125570515, 7124072211203775
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The Hankel transform of this sequence is 6^C(n+1,2). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 28 2007
The Hankel transform of the sequence starting 1, 1, 3, 15, ... is A081955. [From Paul Barry (pbarry(AT)wit.ie), Dec 09 2008]
Number of Schroeder paths from (0,0) to (0,2n) allowing two colours for the down steps (or alternatively for the rise steps). [From Paul Barry (pbarry(AT)wit.ie), Feb 01 2009]
Essentially reversion of x(1-2x)/(1+x). [From Paul Barry (pbarry(AT)wit.ie), Apr 28 2009]
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LINKS
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E. Ackerman, G. Barequet, R. Y. Pinter and D. Romik, The number of guillotine partitions in d dimensions
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FORMULA
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G.f.: [1-z-(z^2-10z+1)^(1/2)]/(4z).
a(n)=sum{k=0..n, C(n+k, 2k)2^k*C(k)}, C(n) given by A000108. - Paul Barry (pbarry(AT)wit.ie), May 21 2005
a(n)=Sum_{k, 0<=k<=n}A060693(n,k)*2^(n-k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 02 2007
a(0)=1, a(n)=a(n-1)+2*Sum_{k, 0<=k<=n-1}a(k)*a(n-1-k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 23 2007
a(n)=(3/2)*A107841(n) for n>0 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 28 2007
G.f.: 1/(1-x-2x/(1-x-2x/(1-x-2x/(1-.... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), Feb 01 2009]
G.f.: 1/(1-3x-6x^2/(1-5x-6x^2/(1-5x-6x^2/(1-... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), Apr 28 2009]
G.f.: 1/(1-3x/(1-2x/(1-3x/(1-2x/(1-3x/(1-... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), May 14 2009]
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CROSSREFS
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Third column of array A103209.
Sequence in context: A020108 A002893 A074539 this_sequence A060066 A128240 A076301
Adjacent sequences: A103207 A103208 A103209 this_sequence A103211 A103212 A103213
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan, Jan 27 2005
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