A117271 Column 0 of triangle A117270, which is the matrix log of triangle A117269.

0, 1, 2, 12, 134, 2100, 42302, 1041852, 30331814, 1019056260, 38805685262, 1651676734092, 77703508288694, 4003868870257620, 224255353667365022, 13565588100060643932, 881405810330856632774, 61218510507062012550180

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

E.g.f.: A(x) = log( (3-sqrt(5-4*exp(x)))/2 ).

a(n) ~ sqrt(10) * n^(n-1) / (6 * exp(n) * (log(5)-2*log(2))^(n-1/2)). - Vaclav Kotesovec, Feb 25 2014

Prog

(PARI) {a(n)=local(C=matrix(n+1, n+1, r, c, if(r>=c, binomial(r-1, c-1))), M=C, L); for(i=1, n+1, M=(M-M^0)^2+C); L=sum(r=1, #M, -(M^0-M)^r/r); return(L[n+1, 1])}

Crossrefs

Cf. A117269, A117270.

Sequence in context: A080487 A077696 A326361 * A289998 A180353 A208873

Adjacent sequences: A117268 A117269 A117270 * A117272 A117273 A117274

Keyword

nonn

Author

Paul D. Hanna, Mar 05 2006

Status

approved