A376551 This sequence satisfies: n = Sum_{k=0..n} ((-n)^(n - k)*binomial(n, k)*a(k)).

0, 1, 6, 30, 164, 980, 6342, 44254, 331144, 2642472, 22379210, 200311034, 1887949164, 18676191196, 193352093326, 2089583250990, 23519349939728, 275137968890576, 3339075981451410, 41967997127203042, 545452423113576820, 7320310586184404676, 101314914535943061206, 1444341387745444125590, 21185535150823665972120, 319401932972290702809400

Offset: 0

Author

Thomas Scheuerle, Nov 27 2024

Keywords

• nonn
• easy

Crossrefs

Cf. A000248, A185298.

Programs

PARI

a(max_n) = {my(x='x+O('x^(max_n+1))); concat([0], Vec(serlaplace(x*exp(x)*exp(x*exp(x))*(1+x))))}

PARI

a(n) = n*sum(k=0, n, binomial(n, k)*(n-k)^k)

Formula

E.g.f.: x*exp(x)*exp(x*exp(x))*(x+1).

a(n) = A000248(n)*n.

a(n) = n*Sum_{k=0..n} (binomial(n, k)*(n - k)^k).