A357392 E.g.f. satisfies A(x) = -log(1 - x * exp(2 * A(x))).

0, 1, 5, 56, 990, 24024, 742560, 27907200, 1235591280, 62990928000, 3634245014400, 234102016512000, 16654322805120000, 1296884927852236800, 109720581991308288000, 10021650950985427353600, 982869376029609100032000, 103017324974226408345600000

Offset

0,3

Links

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

Formula

E.g.f. satisfies A(x) = log(1 + x * exp(3 * A(x))).

a(n) = Sum_{k=1..n} (2 * n)^(k-1) * |Stirling1(n,k)|.

a(n) = Sum_{k=1..n} (3 * n)^(k-1) * Stirling1(n,k).

a(n) = Product_{k=2*n+1..3*n-1} k = (3*n-1)!/(2*n)! for n > 0.

Prog

(PARI) a(n) = sum(k=1, n, (2*n)^(k-1)*abs(stirling(n, k, 1)));
(PARI) a(n) = sum(k=1, n, (3*n)^(k-1)*stirling(n, k, 1));
(PARI) a(n) = if(n==0, 0, (3*n-1)!/(2*n)!);

Crossrefs

Cf. A006963, A357393.

Cf. A357333, A357338.

Sequence in context: A006293 A367155 A298689 * A217817 A217818 A217819

Adjacent sequences: A357389 A357390 A357391 * A357393 A357394 A357395

Keyword

nonn

Author

Seiichi Manyama, Sep 26 2022

Status

approved