A340837 a(n) = (1/2) * Sum_{k>=0} (k*(k - 1))^n / 2^k.

1, 2, 52, 3272, 382672, 71819552, 19755648832, 7489898916992, 3743721038908672, 2385494267756237312, 1887436919680269939712, 1815491288416066631616512, 2086364959404184854563049472, 2823211429546048668686123343872, 4443155724532239407325655263035392

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..n} (-1)^k * binomial(n,k) * A000670(2*n-k).

a(n) = 2 * A080163(n) for n > 0. - Hugo Pfoertner, Jan 23 2021

a(n) = A122101(2*n,n). - Alois P. Heinz, Jun 23 2023

Mathematica

Table[(1/2) Sum[(k (k - 1))^n/2^k, {k, 0, Infinity}], {n, 0, 14}]
Table[(1/2) Sum[(-1)^k Binomial[n, k] HurwitzLerchPhi[1/2, k - 2 n, 0], {k, 0, n}], {n, 0, 14}]

Crossrefs

Cf. A000670, A020556, A052841, A080163, A098696, A122101, A249938.

Sequence in context: A099882 A216611 A246485 * A121293 A246743 A057106

Adjacent sequences: A340834 A340835 A340836 * A340838 A340839 A340840

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 23 2021

Status

approved