A274387 - OEIS

%I #20 Jun 27 2016 03:30:52

%S 1,1,3,43,1345,71721,5787931,656778529,99609347825,19451450431009,

%T 4752356577301171,1419957082098657081,509327639955159790777,

%U 215968308944943346029577,106859555896120941092549371,61015970334444558798467062801,39820542372512292977427634794721,29454908124155520098406206592241281,24512125500202005940687498958550124771,22799363145943007981544986753209784020249,23563018240183207044471748499194925348436201

%N A diagonal of rectangular array A274391 of coefficients in functions that satisfy W_n(x) = W_{n-1}(x)^W_n(x), with W_0(x) = exp(x).

%C a(0) = 1 by convention. All terms appear to be odd.

%H Paul D. Hanna and Vaclav Kotesovec, <a href="/A274387/b274387.txt">Table of n, a(n) for n = 0..200</a> (terms 0..100 from Paul D. Hanna)

%F a(n) ~ c * (n-1)! * n! * exp(n), where c = 0.172... . - _Vaclav Kotesovec_, Jun 27 2016

%o (PARI) {ITERATE(F,n,k) = my(G=x +x*O(x^k)); for(i=1,n,G=subst(G,x,F));G}

%o {A274391(n,k) = my(TREE = serreverse(x*exp(-x +x*O(x^k)))); k!*polcoeff(exp(ITERATE(TREE,n,k)),k)}

%o /* Print table A274391 */

%o for(n=0,10,for(k=0,10,print1(A274391(n,k),", "));print("..."))

%o /* Print this sequence as a diagonal in A274391 */

%o for(n=0,20,print1(A274391(n-1,n),", "))

%Y Cf. A274391, A274388.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jun 24 2016