A249459 -id:A249459 - cp's OEIS frontend

A350008 a(n) = Sum_{k=0..n} k^(2*k).

1, 2, 18, 747, 66283, 9831908, 2186614244, 680409687093, 282155386397749, 150376790683396870, 100150376790683396870, 81502899763630444510191, 79578350103154474577951727, 91812908543371771132977567736

Offset: 0

Seiichi Manyama, Dec 08 2021

nonn

Partial sums of A062206.

Seiichi Manyama, Table of n, a(n) for n = 0..214

Cf. A000330, A062206, A062970, A100262, A249459, A349962.

a[n_] := Sum[If[k == 0, 1, k^(2*k)], {k, 0, n}]; Array[a, 14, 0] (* Amiram Eldar, Dec 08 2021 *)

PARI
```
a(n) = sum(k=0, n, k^(2*k));
```

a(n) ~ n^(2*n). - Vaclav Kotesovec, Dec 08 2021

A355468 Expansion of Sum_{k>=0} (k^2 * x/(1 - k^2 * x))^k.

Original entry on oeis.org

1, 1, 17, 858, 85988, 14318320, 3570592512, 1245401343760, 578840603221568, 345763649636940672, 258099498410703320960, 235426611021544158413824, 257654470061373320338925568, 333210260028337620911268462592

Offset: 0

Seiichi Manyama, Jul 03 2022

nonn

Winston de Greef, Table of n, a(n) for n = 0..211

Cf. A195242, A242446, A249459.

my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (k^2*x/(1-k^2*x))^k))

a(n) = if(n==0, 1, sum(k=1, n, k^(2*n)*binomial(n-1, k-1)));

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

cp's OEIS Frontend

A350008 a(n) = Sum_{k=0..n} k^(2*k).

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A355468 Expansion of Sum_{k>=0} (k^2 * x/(1 - k^2 * x))^k.

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PARI

Formula