A274387 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).

1, 1, 3, 43, 1345, 71721, 5787931, 656778529, 99609347825, 19451450431009, 4752356577301171, 1419957082098657081, 509327639955159790777, 215968308944943346029577, 106859555896120941092549371, 61015970334444558798467062801, 39820542372512292977427634794721, 29454908124155520098406206592241281, 24512125500202005940687498958550124771, 22799363145943007981544986753209784020249, 23563018240183207044471748499194925348436201

Offset: 0

Author

Paul D. Hanna, Jun 24 2016

Keywords

• nonn

Comments

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

Links

• Paul D. Hanna and Vaclav Kotesovec, Table of n, a(n) for n = 0..200 (terms 0..100 from Paul D. Hanna)

Crossrefs

Cf. A274391, A274388.

Programs

PARI

{ITERATE(F,n,k) = my(G=x +x*O(x^k)); for(i=1,n,G=subst(G,x,F));G}
{A274391(n,k) = my(TREE = serreverse(x*exp(-x +x*O(x^k)))); k!*polcoeff(exp(ITERATE(TREE,n,k)),k)}
/* Print table A274391 */
for(n=0,10,for(k=0,10,print1(A274391(n,k),", "));print("..."))
/* Print this sequence as a diagonal in A274391 */
for(n=0,20,print1(A274391(n-1,n),", "))

Formula

a(n) ~ c * (n-1)! * n! * exp(n), where c = 0.172... . - Vaclav Kotesovec, Jun 27 2016