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A387314
Expansion of 1/((1-x) * (1-9*x))^(7/2).
2
1, 35, 756, 13020, 196266, 2709630, 35148036, 435203340, 5198003811, 60326090825, 683903083864, 7603632658440, 83157463636884, 896739874849980, 9553010933452824, 100690915725416520, 1051393771423717029, 10887352006705432335, 111903813927216900204, 1142507997942276850500
OFFSET
0,2
LINKS
FORMULA
n*a(n) = (10*n+25)*a(n-1) - 9*(n+5)*a(n-2) for n > 1.
a(n) = (-1)^n * Sum_{k=0..n} 9^k * binomial(-7/2,k) * binomial(-7/2,n-k).
a(n) = Sum_{k=0..n} (-8)^k * binomial(-7/2,k) * binomial(n+6,n-k).
a(n) = Sum_{k=0..n} 8^k * 9^(n-k) * binomial(-7/2,k) * binomial(n+6,n-k).
a(n) = (binomial(n+6,3)/20) * A387308(n).
a(n) = (-1)^n * Sum_{k=0..n} 10^k * (9/10)^(n-k) * binomial(-7/2,k) * binomial(k,n-k).
MATHEMATICA
CoefficientList[Series[1/((1-x)*(1-9*x))^(7/2), {x, 0, 33}], x] (* Vincenzo Librandi, Aug 28 2025 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(1/((1-x)*(1-9*x))^(7/2))
(Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := 1/((1-x) * (1-9*x))^(7/2); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // Vincenzo Librandi, Aug 28 2025
CROSSREFS
Cf. A387308.
Sequence in context: A326865 A139641 A240928 * A028220 A334909 A028213
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 25 2025
STATUS
approved