A368525 a(n) = Sum_{k=1..n} k^3 * n^(n-k).

0, 1, 10, 60, 364, 2745, 27246, 346864, 5422264, 100449225, 2149062490, 52097910876, 1410401518692, 42153624499441, 1378058477508454, 48900582823143360, 1871456346915007216, 76821658841556480753, 3366451935514051046802, 156839738363103277783900

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = [x^n] x * (1+4*x+x^2)/((1-n*x) * (1-x)^4).

a(n) = n * (n^n * (n^2 + 4*n + 1) - n^5 - 3*n^2 - n - 1)/(n-1)^4 for n > 1.

Prog

(PARI) a(n) = sum(k=1, n, k^3*n^(n-k));

Crossrefs

Cf. A062805, A368505, A368524.

Cf. A368527.

Sequence in context: A083585 A250575 A155633 * A002493 A054364 A004309

Adjacent sequences: A368522 A368523 A368524 * A368526 A368527 A368528

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 28 2023

Status

approved