A364431 G.f. satisfies A(x) = 1 + x*A(x)*(1 + 2*A(x)^3).

1, 3, 27, 351, 5319, 87885, 1535517, 27898101, 521740197, 9977087439, 194191054263, 3834392341779, 76619557946475, 1546479815079321, 31482877148802873, 645689728734541929, 13328555370318744777, 276704344407952939131, 5773556701375333682355

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

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

D-finite with recurrence 3*n*(3*n-1)*(3*n+1)*a(n) +(-458*n^3 +201*n^2 +401*n -216)*a(n-1) +3*(-1105*n^3 +6549*n^2 -11384*n +5796)*a(n-2) +18*(-262*n^3 +2877*n^2 -10295*n +12006)*a(n-3) +27*(n-4)*(31*n^2 -314*n +735)*a(n-4) -81*(10*n-51) *(n-4)*(n-5)*a(n-5) +243*(n-5)*(n-6) *(n-4)*a(n-6)=0. - R. J. Mathar, Jul 25 2023

Maple

A364431 := proc(n)
    add(2^k* binomial(n, k) * binomial(n+3*k+1, n) / (n+3*k+1), k=0..n) ;
end proc:
seq(A364431(n), n=0..70); # R. J. Mathar, Jul 25 2023

Prog

(PARI) a(n) = sum(k=0, n, 2^k*binomial(n, k)*binomial(n+3*k+1, n)/(n+3*k+1));

Crossrefs

Cf. A103210, A348912.

Cf. A364430, A364432.

Sequence in context: A354658 A307650 A168593 * A328182 A372201 A370288

Adjacent sequences: A364428 A364429 A364430 * A364432 A364433 A364434

Keyword

nonn

Author

Seiichi Manyama, Jul 24 2023

Status

approved