A378325 G.f. A(x) = Sum_{n>=0} a(n)*x^n, where a(n) = Sum_{k=0..n-1} [x^k] A(x)^k for n >= 1 with a(0) = 1.

1, 1, 2, 7, 41, 338, 3499, 42969, 606351, 9633640, 169888025, 3290314970, 69409429043, 1584105116525, 38894316619948, 1022411500472240, 28653072049382809, 852911635849385778, 26876978490909421289, 893929164892155754432, 31296785296935394097351, 1150551256823546563078988

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..300

Formula

a(n) ~ c * n! / (n^alpha * LambertW(1)^n), where alpha = 2 - 2*LambertW(1) - 1/(1 + LambertW(1)) = 0.22760967581532... and c = 0.323194722450152336...

Prog

(PARI) {a(n) = my(A=[1]); for(m=1, n, A=concat(A, 0);
A[#A] = 1 + sum(k=1, m-1, (polcoeff(Ser(A)^k, k)) )); A[n+1]}
for(n=0, 30, print1(a(n), ", ")) \\ after Paul D. Hanna

Crossrefs

Cf. A377098, A378326.

Cf. A002212, A307678, A349331, A349332, A349333, A349334, A349335.

Sequence in context: A107376 A220896 A087804 * A006677 A346271 A101390

Adjacent sequences: A378321 A378323 A378324 * A378326 A378327 A378328

Keyword

nonn,new

Author

Vaclav Kotesovec, Nov 23 2024

Status

approved