A367017 G.f. satisfies A(x) = 1 + x*A(x)^5*(1 - x).

1, 1, 4, 25, 185, 1495, 12776, 113534, 1038535, 9713905, 92480570, 893215584, 8730601596, 86198356180, 858388634250, 8611765147660, 86958794304735, 883103159075400, 9013769253136005, 92419535419392485, 951446700812718515, 9831013564639954705

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(k,n-k) * A002294(k).

D-finite with recurrence 8*n*(4*n+1)*(2*n-1)*(4*n-1)*a(n) +(-5429*n^4 +18282*n^3 -25831*n^2 +17298*n -4440)*a(n-1) +2*(19849*n^4 -141024*n^3 +381209*n^2 -464754*n +216120)*a(n-2) +2*(-73689*n^4 +806134*n^3 -3333345*n^2 +6161648*n -4286688)*a(n-3) +8*(39612*n^4 -581510*n^3 +3224355*n^2 -7996990*n +7478448)*a(n-4) +(-412341*n^4 +7529906*n^3 -51862191*n^2 +159663466*n -185354880)*a(n-5) +2*(160399*n^4 -3475600*n^3 +28343735*n^2 -103123250*n +141257856)*a(n-6) +20*(-6875*n^4 +171250*n^3 -1601500*n^2 +6665375*n -10418688)*a(n-7) +40*(5*n-38) *(5*n-32)*(5*n-36)*(5*n-34)*a(n-8)=0. - R. J. Mathar, Mar 02 2026

Prog

(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(k, n-k)*binomial(5*k, k)/(4*k+1));

Crossrefs

Cf. A200753, A367016.

Cf. A002294, A365184.

Sequence in context: A362206 A364759 A246539 * A370473 A369479 A166697

Adjacent sequences: A367014 A367015 A367016 * A367018 A367019 A367020

Keyword

nonn

Author

Seiichi Manyama, Nov 01 2023

Status

approved