A367414 -id:A367414 - cp's OEIS frontend

A367317 Expansion of (1/x) * Series_Reversion( x * (1-x-x^4/(1-x)) ).

1, 1, 2, 5, 15, 50, 177, 649, 2436, 9307, 36080, 141610, 561732, 2248709, 9073415, 36863549, 150676275, 619169360, 2556446520, 10600160707, 44121921044, 184291848864, 772204252280, 3244999395406, 13672564904027, 57749354647408, 244469827514066

Offset: 0

Seiichi Manyama, Jan 26 2024

nonn

Index entries for reversions of series

Cf. A001003, A054515.

Cf. A063021, A367414, A367415.

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

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

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

A367415 Expansion of (1/x) * Series_Reversion( x * (1-x-x^4/(1-x)^3) ).

Original entry on oeis.org

1, 1, 2, 5, 15, 52, 198, 793, 3255, 13529, 56696, 239340, 1017900, 4361840, 18828606, 81833505, 357865215, 1573549667, 6952392450, 30848928525, 137403484655, 614104910096, 2753200345000, 12378494389660, 55799811151140, 252141767612812, 1141894552992368

Offset: 0

Seiichi Manyama, Jan 26 2024

nonn

Index entries for reversions of series

Cf. A063021, A367317, A367414.

my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x-x^4/(1-x)^3))/x)

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

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

A369581 Expansion of (1/x) * Series_Reversion( x / (1+x+x^4/(1+x)^2) ).

Original entry on oeis.org

1, 1, 1, 1, 2, 4, 7, 11, 20, 40, 79, 147, 278, 550, 1110, 2204, 4352, 8708, 17689, 35971, 72933, 148271, 303582, 624132, 1283898, 2643354, 5458457, 11306443, 23460067, 48727689, 101363663, 211262307, 441026328, 921743772, 1928573045, 4040272335, 8474803721

Offset: 0

Seiichi Manyama, Jan 26 2024

nonn

Index entries for reversions of series

Cf. A367414.

my(N=40, x='x+O('x^N)); Vec(serreverse(x/(1+x+x^4/(1+x)^2))/x)

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

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

cp's OEIS Frontend

A367317 Expansion of (1/x) * Series_Reversion( x * (1-x-x^4/(1-x)) ).

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A367415 Expansion of (1/x) * Series_Reversion( x * (1-x-x^4/(1-x)^3) ).

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A369581 Expansion of (1/x) * Series_Reversion( x / (1+x+x^4/(1+x)^2) ).

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