A177410 -id:A177410 - cp's OEIS frontend

A177400 a(n) = binomial(n*2^n, n).

1, 2, 28, 2024, 635376, 820384032, 4281625192384, 89850821311025280, 7571365534761592422144, 2561263066959640762657702400, 3477982739629565890806006777904128

Offset: 0

Paul D. Hanna, Jun 26 2010

nonn

Cf. A177410, A177411.

Cf. A136463. - Paul D. Hanna, Jul 03 2010

Table[Binomial[n 2^n,n],{n,0,20}] (* Harvey P. Dale, Jan 15 2022 *)

PARI
```
{a(n)=binomial(n*2^n,n)}
```

{a(n)=polcoeff(sum(k=0, n, n^k*log(1+2^k*x +x*O(x^n))^k/k!), n)} \\ Paul D. Hanna, Jul 03 2010

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

a(n) = [x^n] Sum_{k=0..n} n^k * log(1 + 2^k*x)^k/k!. - Paul D. Hanna, Jul 03 2010

A177411 a(n) = binomial((n+1)*2^(n+1), n)/(n+1).

Original entry on oeis.org

1, 4, 92, 10416, 5258872, 11297164096, 100955979001152, 3709635244861142784, 556796318904269731012544, 339945532169833436692992549888, 841788571395046141591475043524725760

Offset: 0

Paul D. Hanna, Jun 26 2010

nonn

Cf. A177410, A177400.

Table[Binomial[(n+1)2^(n+1),n]/(n+1),{n,0,20}] (* Harvey P. Dale, Feb 03 2019 *)

PARI
```
{a(n)=binomial((n+1)*2^(n+1),n)/(n+1)}
```

{a(n)=polcoeff(sum(k=0, n, 2^k*(n+1)^(k-1)*log(1+2^k*x +x*O(x^n))^k/k!), n)} \\ Paul D. Hanna, Jul 03 2010

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

a(n) = [x^n] Sum_{k=0..n} 2^k*(n+1)^(k-1) * log(1 + 2^k*x)^k/k!. - Paul D. Hanna, Jul 03 2010

cp's OEIS Frontend

A177400 a(n) = binomial(n*2^n, n).

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A177411 a(n) = binomial((n+1)*2^(n+1), n)/(n+1).

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Author

Keywords

Crossrefs

Programs

Mathematica

PARI

PARI

Formula