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A377200
Expansion of 1/(1 - 4*x/(1-x))^(7/2).
2
1, 14, 140, 1190, 9170, 66122, 454328, 3009050, 19359620, 121664410, 749879508, 4546925922, 27188341530, 160624341990, 939009926520, 5438826037974, 31244200818306, 178173537480330, 1009366349014100, 5684102310204850, 31836106214747590, 177430881586034110
OFFSET
0,2
FORMULA
a(0) = 1; a(n) = 2 * Sum_{k=0..n-1} (7-5*k/n) * a(k).
a(n) = (2*(3*n+4)*a(n-1) - 5*(n-2)*a(n-2))/n for n > 1.
a(n) = Sum_{k=0..n} (-4)^k * binomial(-7/2,k) * binomial(n-1,n-k).
PROG
(PARI) a(n) = sum(k=0, n, (-4)^k*binomial(-7/2, k)*binomial(n-1, n-k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 19 2024
STATUS
approved