A063021 -id:A063021 - cp's OEIS frontend

A365267 G.f. satisfies A(x) = 1 + xA(x)^2(1 + x^3*A(x)).

1, 1, 2, 5, 15, 47, 153, 513, 1763, 6177, 21981, 79224, 288611, 1061019, 3931320, 14666135, 55041855, 207668702, 787225265, 2996851140, 11452198368, 43915195973, 168930713580, 651708006690, 2520840672423, 9774511167507, 37985839339052

Offset: 0

Seiichi Manyama, Aug 30 2023

nonn

Cf. A001002, A071969.

Cf. A063021, A365268.

a(n) = sum(k=0, n\4, binomial(n-3*k, k)*binomial(2*n-5*k+1, n-3*k)/(2*n-5*k+1));

a(n) = Sum_{k=0..floor(n/4)} binomial(n-3*k,k) * binomial(2*n-5*k+1,n-3*k)/(2*n-5*k+1).

A370798 Expansion of (1/x) * Series_Reversion( x/(x+1/(1-x-x^4)) ).

Original entry on oeis.org

1, 2, 5, 15, 52, 200, 824, 3549, 15745, 71343, 328537, 1532838, 7230341, 34425026, 165230211, 798643501, 3884110353, 18993027790, 93325418867, 460562269745, 2281769792691, 11344607718373, 56585135577335, 283067227288767, 1419859530338142, 7139644680794750

Offset: 0

Seiichi Manyama, Mar 02 2024

nonn

Index entries for reversions of series

Cf. A218225, A370797.

Cf. A063021.

my(N=30, x='x+O('x^N)); Vec(serreverse(x/(x+1/(1-x-x^4)))/x)

a(n) = Sum_{k=0..n} binomial(n,k) * b(k), where g.f. B(x) = Sum_{k>=0} b(k)*x^k satisfies B(x) = (1/x) * Series_Reversion( x*(1-x-x^4) ).

cp's OEIS Frontend

A365267 G.f. satisfies A(x) = 1 + xA(x)^2(1 + x^3*A(x)).

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A370798 Expansion of (1/x) * Series_Reversion( x/(x+1/(1-x-x^4)) ).

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PARI

Formula

cp's OEIS Frontend

A365267 G.f. satisfies A(x) = 1 + x*A(x)^2*(1 + x^3*A(x)).

Views

Author

Keywords

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Programs

PARI

Formula

A370798 Expansion of (1/x) * Series_Reversion( x/(x+1/(1-x-x^4)) ).

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

A365267 G.f. satisfies A(x) = 1 + xA(x)^2(1 + x^3*A(x)).