A295773 a(n) = Sum_{k=0..n} binomial(k^2, k).

1, 2, 8, 92, 1912, 55042, 2002834, 87903418, 4514068786, 265401903136, 17575711359576, 1294325676386112, 104913619501093500, 9281271920245432932, 889811788303594625412, 91895379599481072720852, 10170646981621794947354052, 1200909691326112843842751962

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..338

Formula

a(n) ~ exp(n - 1/2) * n^(n - 1/2) / sqrt(2*Pi).

Mathematica

Table[Sum[Binomial[k^2, k], {k, 0, n}], {n, 0, 20}]

Prog

(PARI) a(n) = sum(k=0, n, binomial(k^2, k)); \\ Michel Marcus, Jan 10 2019
(Magma) [&+[Binomial(k^2, k): k in [0..n]]: n in [0..20]]; // Vincenzo Librandi, Jan 10 2019

Crossrefs

Cf. A014062, A226391, A295772, A359665.

Sequence in context: A067964 A102895 A297451 * A319125 A297688 A126429

Adjacent sequences: A295770 A295771 A295772 * A295774 A295775 A295776

Keyword

nonn

Author

Vaclav Kotesovec, Nov 27 2017

Status

approved