A371617 -id:A371617 - cp's OEIS frontend

A371613 G.f. satisfies A(x) = ( 1 + x / (1 - x*A(x)^3) )^2.

1, 2, 3, 16, 83, 460, 2767, 17210, 110308, 723624, 4832363, 32747106, 224619408, 1556484636, 10879744696, 76621739626, 543159825499, 3872610857558, 27752175177823, 199787917082084, 1444171829169939, 10477887409768628, 76275565075016394

Offset: 0

Seiichi Manyama, Mar 29 2024

nonn

Cf. A371615, A371617.

Cf. A365118, A371612.

a(n, r=2, s=1, t=0, u=6) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));

a(n) = Sum_{k=0..n} binomial(6*(n-k)+2,k) * binomial(n-1,n-k)/(3*(n-k)+1).

A371615 G.f. satisfies A(x) = ( 1 + x / (1 - x*A(x)^3)^2 )^2.

Original entry on oeis.org

1, 2, 5, 34, 222, 1622, 12559, 100904, 835322, 7070574, 60922335, 532566850, 4711614912, 42106192680, 379544358032, 3446755447528, 31504896429042, 289619348156494, 2675953520657839, 24836797229730316, 231461661673958896, 2165002179076830442

Offset: 0

Seiichi Manyama, Mar 29 2024

nonn

Cf. A371613, A371617.

a(n, r=2, s=2, t=0, u=6) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));

a(n) = Sum_{k=0..n} binomial(6*(n-k)+2,k) * binomial(n+k-1,n-k)/(3*(n-k)+1).

cp's OEIS Frontend

A371613 G.f. satisfies A(x) = ( 1 + x / (1 - x*A(x)^3) )^2.

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