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A371780
a(n) = Sum_{k=0..floor(n/3)} binomial(5*n+2,n-3*k).
4
1, 7, 66, 681, 7337, 81081, 911153, 10361554, 118881714, 1373402934, 15954079557, 186165866937, 2180501226751, 25620628577083, 301858589475117, 3564841627421691, 42186363329210473, 500142626996777355, 5939062937833796486, 70626949319708756435
OFFSET
0,2
LINKS
FORMULA
a(n) = [x^n] 1/(((1-x)^3-x^3) * (1-x)^(4*n)).
MAPLE
f:= proc(n) local k; add(binomial(5*n+2, n-3*k), k=0..n/3); end proc:
map(f, [$0..100]); # Robert Israel, Apr 22 2024
PROG
(PARI) a(n) = sum(k=0, n\3, binomial(5*n+2, n-3*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 05 2024
STATUS
approved