A359659 a(n) = Sum_{k=0..n} k^(k * (n-k+1)).

1, 2, 6, 45, 1051, 88602, 27121964, 37004504305, 198705527223757, 5595513387083114570, 686714367475480207331582, 468422339816915120237104999421, 1664212116512828935888786624225704855

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..51

Formula

G.f.: Sum_{k>=0} (k * x)^k/(1 - k^k * x).

G.f.: Sum_{k>=0} x^k/(1 - (k+1)^(k+1) * x).

a(n) = A349893(n+1) - 1.

Prog

(PARI) a(n) = sum(k=0, n, k^(k*(n-k+1)));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k*x)^k/(1-k^k*x)))
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-(k+1)^(k+1)*x)))

Crossrefs

Cf. A026898, A349893, A359658.

Cf. A031971, A349836, A349883.

Cf. A003101, A349882.

Sequence in context: A255015 A347984 A229836 * A374874 A370818 A367916

Adjacent sequences: A359656 A359657 A359658 * A359660 A359661 A359662

Keyword

nonn

Author

Seiichi Manyama, Jan 10 2023

Status

approved