A378066 -id:A378066 - cp's OEIS frontend

A378064 a(n) = 5n^4 - 6n^2 + 1. Column 4 of A378066.

1, 0, 57, 352, 1185, 2976, 6265, 11712, 20097, 32320, 49401, 72480, 102817, 141792, 190905, 251776, 326145, 415872, 522937, 649440, 797601, 969760, 1168377, 1396032, 1655425, 1949376, 2280825, 2652832, 3068577, 3531360, 4044601, 4611840, 5236737, 5923072

Offset: 0

Peter Luschny, Nov 17 2024

nonn

Cf. A378066.

Maple
```
seq(5*n^4 - 6*n^2 + 1, n = 0..33);
```

def A378064(n): return (m:=n**2)*(5*m-6)+1 # Chai Wah Wu, Nov 18 2024

a(n) = [x^n] (-57*x^3 - 67*x^2 + 5*x - 1)/(x - 1)^5.

A378063 a(n) = (-2n)^n Euler(n, (n - 1)/(2*n)) for n >= 1, and a(0) = 1. Main diagonal of A378066.

Original entry on oeis.org

1, 1, -3, -26, 1185, 15376, -2749355, -49816976, 22790134017, 533858404096, -498990299504499, -14365294449638912, 23891962452055766497, 816609772823716089856, -2201371244223771530940315, -87139486416935710159898624, 355987789164484245477279893505

Offset: 0

Peter Luschny, Nov 17 2024

sign

Cf. A378066.

a := n -> ifelse(n = 0, 1, (-2*n)^n * euler(n, (n - 1)/(2*n))):
seq(a(n), n = 0..16);

a(n) = Sum_{j=0..n} binomial(n, j)*Euler(j)*(-n)^j.

A378065 a(n) = (-10)^n * Euler(n, 2/5). Row 5 of A378066.

Original entry on oeis.org

1, 1, -24, -74, 2976, 15376, -906624, -6563024, 514546176, 4789470976, -469222938624, -5338232282624, 627559296638976, 8437702651826176, -1157248322241921024, -17953287144063002624, 2814090582404042981376, 49478116534660975230976, -8724885890905288434253824

Offset: 0

Peter Luschny, Nov 17 2024

sign

Cf. A378066.

a := n -> (-10)^n * euler(n, 2/5): seq(a(n), n = 0..18);
# Or:
ser := series(exp(x)/cosh(5*x), x, 20):
seq(n!*coeff(ser, x, n), n = 0..18);

a(n) = n! * [x^n] exp(x)/cosh(5*x).

a(n) = Sum_{j=0..n} (-5)^j*binomial(n, j)*Euler(j).

cp's OEIS Frontend

A378064 a(n) = 5n^4 - 6n^2 + 1. Column 4 of A378066.

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Maple

Python

Formula

A378063 a(n) = (-2n)^n Euler(n, (n - 1)/(2*n)) for n >= 1, and a(0) = 1. Main diagonal of A378066.

Views

Author

Keywords

Crossrefs

Programs

Maple

Formula

A378065 a(n) = (-10)^n * Euler(n, 2/5). Row 5 of A378066.

Views

Author

Keywords

Crossrefs

Programs

Maple

Formula

cp's OEIS Frontend

A378064 a(n) = 5*n^4 - 6*n^2 + 1. Column 4 of A378066.

Views

Author

Keywords

Crossrefs

Programs

Maple

Python

Formula

A378063 a(n) = (-2*n)^n * Euler(n, (n - 1)/(2*n)) for n >= 1, and a(0) = 1. Main diagonal of A378066.

Views

Author

Keywords

Crossrefs

Programs

Maple

Formula

A378065 a(n) = (-10)^n * Euler(n, 2/5). Row 5 of A378066.

Views

Author

Keywords

Crossrefs

Programs

Maple

Formula

A378064 a(n) = 5n^4 - 6n^2 + 1. Column 4 of A378066.

A378063 a(n) = (-2n)^n Euler(n, (n - 1)/(2*n)) for n >= 1, and a(0) = 1. Main diagonal of A378066.