A382537 Expansion of 1/(1 - x*(1 + 4*x)^(5/2)).

1, 1, 11, 51, 211, 1061, 4923, 22765, 107687, 502479, 2352231, 11022911, 51590795, 241559783, 1131156175, 5295875131, 24797055115, 116104311885, 543622665219, 2545347081565, 11917847333151, 55801588711565, 261274518155435, 1223337818786305, 5727913381451455

Offset: 0

Author

Seiichi Manyama, Mar 31 2025

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A362154, A382536, A382538.

Cf. A002422, A382515.

Programs

Magma

R := PowerSeriesRing(Rationals(), 40); f := 1/(1 - x*(1 + 4*x)^(5/2)); seq := [ Coefficient(f, n) : n in [0..30] ];seq; // Vincenzo Librandi, Apr 02 2025

Mathematica

Table[Sum[4^(n-k)*Binomial[5*k/2,n-k],{k,0,n}],{n,0,25}] (* Vincenzo Librandi, Apr 02 2025 *)

PARI

a(n) = sum(k=0, n, 4^(n-k)*binomial(5*k/2, n-k));

Formula

a(n) = Sum_{k=0..n} 4^(n-k) * binomial(5*k/2,n-k).