A385691 -id:A385691 - cp's OEIS frontend

A385725 E.g.f. A(x) satisfies A(x) = exp( x(A(x) + A(ix) + A(-x) + A(-i*x))/4 ), where i is the imaginary unit.

1, 1, 1, 1, 1, 6, 31, 106, 281, 3160, 29701, 176056, 768241, 12702704, 173361371, 1466276176, 8937060081, 195180709248, 3494232292681, 38426220716416, 301057954180801, 8174141246647552, 181144607099402871, 2452803139819922176, 23494461553739152201, 762800754226165963776

Offset: 0

Seiichi Manyama, Jul 08 2025

nonn

Cf. A000272, A058014, A385691.

Cf. A118968.

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

A386202 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n-1,3k) a(3k) a(n-1-3*k).

Original entry on oeis.org

1, 1, 1, 1, 2, 6, 16, 52, 234, 1018, 4724, 27864, 166816, 1018096, 7421220, 56215420, 427276280, 3714931512, 33908654224, 309043657936, 3126424467816, 33317327728936, 354276443249552, 4093007897140128, 49813497858533344, 605442506092221760, 7871720463184084560

Offset: 0

Seiichi Manyama, Jul 14 2025

nonn

Cf. A000111, A000142, A386203.

Cf. A124753, A385691.

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\3, binomial(i-1, 3*j)*v[3*j+1]*v[i-3*j])); v;

E.g.f. A(x) satisfies A'(x) = A(x) * (A(x) + A(w*x) + A(w^2*x))/3, where w = exp(2*Pi*i/3).

cp's OEIS Frontend

A385725 E.g.f. A(x) satisfies A(x) = exp( x(A(x) + A(ix) + A(-x) + A(-i*x))/4 ), where i is the imaginary unit.

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Formula

A386202 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n-1,3k) a(3k) a(n-1-3*k).

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Author

Keywords

Crossrefs

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PARI

Formula

cp's OEIS Frontend

A385725 E.g.f. A(x) satisfies A(x) = exp( x*(A(x) + A(i*x) + A(-x) + A(-i*x))/4 ), where i is the imaginary unit.

Views

Author

Keywords

Crossrefs

Formula

A386202 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n-1,3*k) * a(3*k) * a(n-1-3*k).

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

A385725 E.g.f. A(x) satisfies A(x) = exp( x(A(x) + A(ix) + A(-x) + A(-i*x))/4 ), where i is the imaginary unit.

A386202 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n-1,3k) a(3k) a(n-1-3*k).