A381867 -id:A381867 - cp's OEIS frontend

A381943 G.f. A(x) satisfies A(x) = B(x*A(x)) / (1 - x)^2, where B(x) is the g.f. of A001764.

1, 3, 11, 60, 425, 3426, 29619, 267738, 2497889, 23866056, 232325475, 2295889266, 22971682893, 232248775669, 2368969672183, 24348849065860, 251930963865061, 2621914660411919, 27428338267887815, 288258167672381602, 3042002859317810001, 32222429872821051817

Offset: 0

Seiichi Manyama, Mar 10 2025

nonn

Partial sums of A364592.
Cf. A086616, A381867, A381945.
Cf. A001764.

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

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

A381945 G.f. A(x) satisfies A(x) = B(x*A(x)) / (1 - x)^2, where B(x) is the g.f. of A002293.

Original entry on oeis.org

1, 3, 12, 79, 695, 6961, 74679, 837336, 9689234, 114822820, 1386402276, 16994276781, 210919650044, 2645218761934, 33470438908615, 426758782807956, 5477657372957314, 70720821402587371, 917801926609131194, 11966203939448781600, 156662012236067711036, 2058709975008385135863

Offset: 0

Seiichi Manyama, Mar 10 2025

nonn

Cf. A086616, A381867, A381943.

Cf. A002293.

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

a(n) = Sum_{k=0..n} binomial(5*k+1,k) * binomial(n+k+1,n-k)/(5*k+1).

cp's OEIS Frontend

A381943 G.f. A(x) satisfies A(x) = B(x*A(x)) / (1 - x)^2, where B(x) is the g.f. of A001764.

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