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URL: https://oeis.org/A387315

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A387315
Expansion of 1/((1-x) * (1-13*x))^(5/2).
2
1, 35, 825, 16415, 297220, 5067972, 82893720, 1315073760, 20381376015, 310101196405, 4648184007467, 68817616687365, 1008344472704660, 14644604899082620, 211073938188085620, 3022082811670829676, 43017189132931007655, 609159438493806780405, 8586490781973282553375
OFFSET
0,2
LINKS
FORMULA
n*a(n) = (14*n+21)*a(n-1) - 13*(n+3)*a(n-2) for n > 1.
a(n) = (-1)^n * Sum_{k=0..n} 13^k * binomial(-5/2,k) * binomial(-5/2,n-k).
a(n) = Sum_{k=0..n} (-12)^k * binomial(-5/2,k) * binomial(n+4,n-k).
a(n) = Sum_{k=0..n} 12^k * 13^(n-k) * binomial(-5/2,k) * binomial(n+4,n-k).
a(n) = (binomial(n+4,2)/6) * A387310(n).
a(n) = (-1)^n * Sum_{k=0..n} 14^k * (13/14)^(n-k) * binomial(-5/2,k) * binomial(k,n-k).
MATHEMATICA
CoefficientList[Series[1/((1-x)*(1-13*x))^(5/2), {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))^(5/2))
(Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := 1/((1-x) * (1-13*x))^(5/2); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // Vincenzo Librandi, Aug 28 2025
CROSSREFS
Cf. A387230.
Sequence in context: A249884 A223957 A109508 * A267834 A001724 A062194
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 25 2025
STATUS
approved