A382435 a(n) = Sum_{k=0..n} ( binomial(n,k) - binomial(n,k-1) )^6.
1, 1, 3, 129, 1587, 39443, 1125383, 30211457, 1107074979, 36214609683, 1433494688871, 54495716261011, 2275005440977063, 95146470595975399, 4170974287982618639, 185640304224109725569, 8492643748223480148419, 395051289603660979274339, 18726850582009755291702599
Offset: 0
Keywords
Programs
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Maple
b:= proc(x, y) option remember; `if`(y<0 or y>x, 0, `if`(x=0, 1, add(b(x-1, y+j), j=[-1, 1]))) end: a:= n-> 2*add(b(n, n-2*j)^6, j=0..n/2)-1: seq(a(n), n=0..18); # Alois P. Heinz, Mar 25 2025 -
PARI
a(n) = sum(k=0, n, (binomial(n, k)-binomial(n, k-1))^6);
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Python
from math import comb def A382435(n): return (sum((comb(n,j)*(m:=n-(j<<1)+1)//(m+j))**6 for j in range((n>>1)+1))<<1)-1 # Chai Wah Wu, Mar 25 2025