John H. Chakkour - cp's OEIS frontend

A341330 a(n) = Sum_{k=1..n} (-k)^(k+1).

1, -7, 74, -950, 14675, -265261, 5499540, -128718188, 3358066213, -96641933787, 3041786442934, -103951418936138, 3833424966763151, -151734670591049073, 6416673685121841552, -288731231494230984304, 13774353220573494006705, -694460992134764182350927

Offset: 1

John H. Chakkour, Feb 09 2021

sign

Cf. A007778, A062815.

Mathematica
```
Accumulate[(-#)^(#+1)&/@Range[17]]
```
PARI
```
a(n) = sum(i=1, n, (-i)^(i+1));
```

sum = 0
for i in range(1,20):
    sum += (-i)**(i+1)
    print(sum, end = ", ")

A309372 a(n) = n^2 - n^3 + n^4.

Original entry on oeis.org

0, 1, 12, 63, 208, 525, 1116, 2107, 3648, 5913, 9100, 13431, 19152, 26533, 35868, 47475, 61696, 78897, 99468, 123823, 152400, 185661, 224092, 268203, 318528, 375625, 440076, 512487, 593488, 683733, 783900, 894691, 1016832, 1151073, 1298188, 1458975, 1634256, 1824877, 2031708, 2255643, 2497600

Offset: 0

John H. Chakkour, Aug 02 2019

			a(4) = 4^2 - 4^3 + 4^4 = 16 - 64 + 256 = 208.

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Cf. A132998.

concat(0, Vec(x*(1 + 3*x)*(1 + 4*x + x^2) / (1 - x)^5 + O(x^40))) \\ Colin Barker, Aug 11 2019

for x in range(100):
    print((x**2)-(x**3)+(x**4))

From Colin Barker, Aug 11 2019: (Start)
G.f.: x*(1 + 3*x)*(1 + 4*x + x^2) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)

A308507 a(n) = (a(n-1) + a(n-2))^4, for n >= 2; a(0)=0, a(1)=1.

Original entry on oeis.org

0, 1, 1, 16, 83521, 48698490414981476161, 5624216052381164150697569400035392464306474190030694298257503425709420810383376

Offset: 0

John H. Chakkour, Jun 02 2019

			a(4) = (a(3) + a(2))^4 = (16 + 1)^4 = 83521.

Cf. A000045, A014253, A134923.

RecurrenceTable[{a[0]==0, a[1]==1, a[n]==(a[n-1]+a[n-2])^4}, a, {n, 10}]

f0 = 0
f1 = 1
next_val = (f0+f1)**4
i = 0
while i <= 10:
     next_val = (f0+f1)**4
     f0 = f1
     f1 = next_val
     i = i+1
     print(next_val)

cp's OEIS Frontend

User: John H. Chakkour

A341330 a(n) = Sum_{k=1..n} (-k)^(k+1).

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A309372 a(n) = n^2 - n^3 + n^4.

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Python

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A308507 a(n) = (a(n-1) + a(n-2))^4, for n >= 2; a(0)=0, a(1)=1.

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Author

Keywords

Examples

Crossrefs

Programs

Mathematica

Python