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Search: id:A054443
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| 1, 4, 14, 40, 109, 276, 682, 1624, 3810, 8744, 19868, 44496, 98941, 217780, 476786, 1036024, 2241814, 4823160, 10342180, 22076080, 46994386, 99673224, 210923364, 445000560, 937051684, 1968204496, 4127285688
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OFFSET
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0,2
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FORMULA
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a(2*k)= (2*k+7)*4^(k+1)-binomial(2*(k+2), k+2)*(4*k+9)/2, a(2*k+1)= (k+4)*4^(k+2)-(k+3)*binomial(2*(k+3), k+3), k >= 0.
a(n)= A054336(n+3, 3) (fourth column of convolution triangle). G.f.: (1/(1-x-x^2*c(x^2)))^4, with c(x) the g.f. for the Catalan numbers A000108.
G.f.: (c(x/(2x-1))/(1-2x))^4 . - Michael Somos Jul 31 2005
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PROGRAM
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(PARI) {a(n)=local(k); if(n<0, 0, k=n\2; if(n%2, (k+4)*4^(k+2)-(k+3)*binomial(2*(k+3), k+3), (2*k+7)*4^(k+1)-binomial(2*(k+2), k+2)*(4*k+9)/2 ))}
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CROSSREFS
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Cf. A000108, A001405, A054336, A054442.
Sequence in context: A121593 A023003 A001872 this_sequence A072674 A032285 A132357
Adjacent sequences: A054440 A054441 A054442 this_sequence A054444 A054445 A054446
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KEYWORD
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easy,nonn
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Mar 27 2000
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