def arec(top):
ret = 0
if top==0:return e-1
for n in range(1,top+1):
ret+=arec(top-n)/fact(n)
ret+=(e-1)-sum([1/fact(i) for i in range(1,top+1)])
return ret
def a(n):
if n==0:return e-1
if n==1:return 2*e-3
if n==2:return 7/2*e-6
if n<0:return 1
x = 0
i = 1
while True:
lastx,x = x,x+a(n-i)/fact(i)
i+=1
if lastx==x:return x
def Euler_20(num = 100):
f = maths.fact(100)
ret = maths.sumdigs(f)
return ret
def e020(num=100):
return sum([int(i) for i in str(fact(num))])
def test():
for i in range(100,9101,100):
print(i/9100,end='\r')
x = abi(i)
return abi(9100)+(-2*abi(9100)+fact(9100))
def Bval(n):
return fact(n)-2*A(n)
def B1(n):
return round(fact(n)-2*D(n))
def D(n):
if n<0:return 0
return round((fact(n)*b(n))/(e-2))
def bbi(n,a = 0):
if a:
return fact(n)-2*a
else:
return fact(n)-2*abi(n)
def abi(n):
ret = fact(n)
for i in range(n):
ret+=bc(n,i)*abi(i)
return ret
def Euler_15(i=20,j=20):
ret = maths.fact(i+j)//maths.fact(i)//maths.fact(j)#binomial coefficients
return ret
def Euler_15(i=20, j=20):
ret = maths.fact(i + j) // maths.fact(i) // maths.fact(
j) #binomial coefficients
return ret