A171187 a(n) = Sum_{k=0..[n/2]} A034807(n,k)^n, where A034807 is a triangle of Lucas polynomials.

1, 1, 5, 28, 273, 6251, 578162, 107060591, 29911744769, 27309372325966, 100510174785157275, 579282314757603925315, 5692451844585536053973346, 272831740026972379247127727751, 36494329378701187545939734030067963

Offset

0,3

Links

Table of n, a(n) for n=0..14.

Formula

a(n) = Sum_{k=0..[n/2]} [C(n-k,k) + C(n-k-1,k-1)]^n.

Ignoring the zeroth term, equals the logarithmic derivative of A171186.

Example

The n-th term equals the sum of the n-th powers of the n-th row of triangle A034807:
a(0) = 2^0 = 1;
a(1) = 1^1 = 1;
a(2) = 1^2 + 2^2 = 5;
a(3) = 1^3 + 3^3 = 28;
a(4) = 1^4 + 4^4 + 2^4 = 273;
a(5) = 1^5 + 5^5 + 5^5 = 6251;
a(6) = 1^6 + 6^6 + 9^6 + 2^6 = 578162;
a(7) = 1^7 + 7^7 + 14^7 + 7^7 = 107060591; ...

Prog

(PARI) {a(n)=sum(k=0, n\2, (binomial(n-k, k)+binomial(n-k-1, k-1))^n)}

Crossrefs

Cf. A171186, A034807, A067961.

Sequence in context: A320974 A339712 A023887 * A354899 A057792 A338661

Adjacent sequences: A171184 A171185 A171186 * A171188 A171189 A171190

Keyword

nonn

Author

Paul D. Hanna, Dec 13 2009

Status

approved