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A112696
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Partial sum of Catalan numbers A000108 multiplied by powers of 2.
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1
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1, 3, 11, 51, 275, 1619, 10067, 64979, 431059, 2920403, 20119507, 140513235, 992530387, 7078367187, 50896392147, 368577073107, 2685777334227, 19678579249107, 144888698621907, 1071443581980627, 7954422715502547
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n)=sum(C(k)*2^k, k=0..n), n>=0, with C(n):=A000108(n).
G.f.: c(2*x)/(1-x), where c(x):=(1-sqrt(1-4*x))/(2*x) is the o.g.f. of Catalan numbers A000108.
sum((binomial(2*j,j))*2^j/(j+1),j=0..n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 26 2006
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MAPLE
| a:=n->sum((binomial(2*j, j))*2^j/(j+1), j=0..n): seq(a(n), n=0..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 26 2006
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CROSSREFS
| Third column (m=2) of triangle A112705.
Sequence in context: A199212 A113283 A127784 * A192925 A132006 A020043
Adjacent sequences: A112693 A112694 A112695 * A112697 A112698 A112699
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Oct 31 2005
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