A382538 Expansion of 1/(1 - x*(1 + 4*x)^(7/2)).
1, 1, 15, 99, 519, 3165, 19503, 115053, 688803, 4141863, 24778355, 148376447, 889216143, 5326274463, 31903872267, 191123789739, 1144894457103, 6858232252437, 41083285178247, 246102886383661, 1474237118571467, 8831178384769525, 52901735792001759
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..600
Programs
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Magma
R
:=PowerSeriesRing(Rationals(), 28); Coefficients(R!( 1/(1 - x*(1 + 4*x)^(7/2)))); // Vincenzo Librandi, May 16 2025 -
Mathematica
Table[Sum[4^(n-k)* Binomial[7*k/2, n-k],{k,0,n}],{n,0,28}] (* Vincenzo Librandi, May 16 2025 *) -
PARI
a(n) = sum(k=0, n, 4^(n-k)*binomial(7*k/2, n-k));
Formula
a(n) = Sum_{k=0..n} 4^(n-k) * binomial(7*k/2,n-k).
D-finite with recurrence (-n+1)*a(n) +2*(-2*n+11)*a(n-1) +(n-1)*a(n-2) +2*(16*n-25)*a(n-3) +56*(8*n-17)*a(n-4) +224*(16*n-43)*a(n-5) +4480*(4*n-13)*a(n-6) +3584*(16*n-61)*a(n-7) +14336*(8*n-35)*a(n-8) +8192*(16*n-79)*a(n-9) +32768*(2*n-11)*a(n-10)=0. - R. J. Mathar, Apr 02 2025