A381785 -id:A381785 - cp's OEIS frontend

A381787 G.f. A(x) satisfies A(x) = (1 + x) * C(x*A(x)), where C(x) is the g.f. of A000108.

1, 2, 5, 22, 112, 623, 3664, 22405, 141002, 907228, 5940663, 39459873, 265228359, 1800608563, 12328843910, 85040632504, 590371016188, 4121775003434, 28921911896836, 203854515625194, 1442669458817907, 10247020573880520, 73024240955785936, 521973882076798493

Offset: 0

Seiichi Manyama, Mar 07 2025

nonn

Cf. A167422, A381785, A381786.

Cf. A000108.

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

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

A381938 G.f. A(x) satisfies A(x) = (1 + x)^2 * B(x*A(x)), where B(x) is the g.f. of A001764.

Original entry on oeis.org

1, 3, 9, 52, 380, 3066, 26304, 235314, 2170312, 20487963, 196988392, 1922327792, 18990571724, 189548947601, 1908604524752, 19364096602370, 197761735366804, 2031444188437719, 20974821788118024, 217561484977675026, 2265961977605950416, 23688432825547509283

Offset: 0

Seiichi Manyama, Mar 10 2025

nonn

Cf. A366694, A367640, A381941.

Cf. A001764, A381785.

a(n) = sum(k=0, n, binomial(4*k+1, k)*binomial(2*k+2, n-k)/(4*k+1));

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

a(n) = A381785(n) + A381785(n-1).

cp's OEIS Frontend

A381787 G.f. A(x) satisfies A(x) = (1 + x) * C(x*A(x)), where C(x) is the g.f. of A000108.

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