A369024 Expansion of (1/x) * Series_Reversion( x * (1-2*x)^4 / (1-x) ).

1, 7, 81, 1135, 17617, 291479, 5038177, 89901023, 1643514849, 30623478951, 579444828465, 11103818394447, 215053322179121, 4202849976054583, 82778942956393409, 1641477474636943295, 32743892109730116801, 656612555241354578759, 13228883898856161274129

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..749

Index entries for reversions of series

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(4*n+k+3,k) * binomial(4*n+2,n-k).

D-finite with recurrence -2*(462919*n-251445)*(4*n+1) *(2*n+1)*(4*n+3) *(n+1)*a(n) +(625365036*n^5 +403579400*n^4 -437229300*n^3 +49132810*n^2 -20878971*n +3771675)*a(n-1) +(484851248*n^5 -3077382030*n^4 +7964893000*n^3 -10232074140*n^2 +6398384592*n -1533654945)*a(n-2) +(652184*n-451475)*(4*n-9) *(n-2)*(4*n-7)*(2*n-3)*a(n-3)=0. - R. J. Mathar, Jan 25 2024

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-2*x)^4/(1-x))/x)
(PARI) a(n, s=1, t=4, u=-1) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);

Crossrefs

Cf. A344553, A369023.

Sequence in context: A364322 A339710 A112119 * A379856 A371027 A058575

Adjacent sequences: A369021 A369022 A369023 * A369025 A369026 A369027

Keyword

nonn

Author

Seiichi Manyama, Jan 12 2024

Status

approved