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URL: https://oeis.org/A387316

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A387316
Expansion of 1/((1-x) * (1-13*x))^(7/2).
2
1, 49, 1498, 36750, 792246, 15681666, 292137846, 5201141946, 89399571261, 1494080348761, 24403114463728, 391038174645664, 6165638429715492, 95880046644705876, 1473241291627666488, 22401020288076984120, 337479336374849120991, 5042656883996693680719
OFFSET
0,2
LINKS
FORMULA
n*a(n) = (14*n+35)*a(n-1) - 13*(n+5)*a(n-2) for n > 1.
a(n) = (-1)^n * Sum_{k=0..n} 13^k * binomial(-7/2,k) * binomial(-7/2,n-k).
a(n) = Sum_{k=0..n} (-12)^k * binomial(-7/2,k) * binomial(n+6,n-k).
a(n) = Sum_{k=0..n} 12^k * 13^(n-k) * binomial(-7/2,k) * binomial(n+6,n-k).
a(n) = (binomial(n+6,3)/20) * A387311(n).
a(n) = (-1)^n * Sum_{k=0..n} 14^k * (13/14)^(n-k) * binomial(-7/2,k) * binomial(k,n-k).
MATHEMATICA
CoefficientList[Series[1/((1-x)*(1-13*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)*(1-13*x))^(7/2))
(Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := 1/((1-x) * (1-13*x))^(7/2); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // Vincenzo Librandi, Aug 28 2025
CROSSREFS
Sequence in context: A012238 A036226 A032655 * A001458 A004374 A203500
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 25 2025
STATUS
approved