A382040 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*exp(4*x)) ).

1, 1, 12, 198, 4912, 163120, 6796224, 341366704, 20088997632, 1356164492544, 103333898644480, 8773563043734016, 821474949840482304, 84093840447771701248, 9344359942839980900352, 1120159940123276849141760, 144096985208727744665288704, 19800296439825918648654561280

Offset

0,3

Links

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

Formula

E.g.f. A(x) satisfies A(x) = 1 + x*A(x)^2*exp(4*x*A(x)).

a(n) = (1/(n+1)) * Sum_{k=0..n} (4*k)^(n-k) * (n+k)!/(k! * (n-k)!).

Prog

(PARI) a(n) = sum(k=0, n, (4*k)^(n-k)*(n+k)!/(k!*(n-k)!))/(n+1);

Crossrefs

Cf. A213644, A379690, A382039.

Cf. A366234, A382031.

Sequence in context: A115865 A291285 A159359 * A119864 A036240 A346509

Adjacent sequences: A382037 A382038 A382039 * A382042 A382043 A382044

Keyword

nonn,new

Author

Seiichi Manyama, Mar 13 2025

Status

approved