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Search: id:A062992
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| 1, 3, 13, 67, 381, 2307, 14589, 95235, 636925, 4341763, 30056445, 210731011, 1493303293, 10678370307, 76957679613, 558403682307, 4075996839933, 29909606989827, 220510631755773, 1632599134961667, 12133359132082173
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OFFSET
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0,2
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COMMENT
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a(n)=N(2; n,x=-1), with the polynomials N(2; n,x) defined in A062991.
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FORMULA
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a(n)=2*sum(((-1)^j)*C(n-j)*2^(n-j), j=0..n)-(-1)^n with C(n) := A000108(n) (Catalan).
G.f.: (2*c(2*x)-1)/(1+x) with c(x) g.f. of A000108.
a(n)=(1/(n+1))*sum{k=0..n, binomial(2n+2, n-k)*binomial(n+k, k)}; - Paul Barry (pbarry(AT)wit.ie), May 11 2005
Rewritten: a(n)= (1-2*c(n, -2))*(-1)^(n+1), n>=0, with c(n, x):=sum(C(k)*x^k, k=0..n) and C(k):=A000108(k) (Catalan). W. Lang Oct 31 2005.
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PROGRAM
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(PARI) a(n)=polcoeff((1-2*x-sqrt(1-8*x+x^2*O(x^n)))/(2*x+2*x^2), n)
(PARI) a(n)=if(n<0, 0, polcoeff(serreverse((x-x^2)/(1+x)^2+O(x^(n+2))), n+1)) (from R. Stephan)
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CROSSREFS
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Cf. A064062.
Cf. A112707 (c(n, -m) triangle). Here m=2 is used.
Sequence in context: A142979 A136784 A027277 this_sequence A064062 A114191 A107592
Adjacent sequences: A062989 A062990 A062991 this_sequence A062993 A062994 A062995
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jul 12 2001
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