A177411 -id:A177411 - 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

A177410 a(n) = binomial((n+1)*2^n, n)/(n+1).

Original entry on oeis.org

1, 2, 22, 1240, 316316, 343855008, 1551088459936, 28684932916796288, 2161788213413182113760, 661624062463590275090838016, 820418024446932078541699530057216

Offset: 0

Paul D. Hanna, Jun 26 2010

nonn

Cf. A177411, A177400.

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

{a(n)=polcoeff(sum(k=0, n, (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)/(n+1).

a(n) = [x^n] Sum_{k=0..n} (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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A177410 a(n) = binomial((n+1)*2^n, n)/(n+1).

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Formula