A369502
Expansion of (1/x) * Series_Reversion( x / ((1+x)^2+x)^2 ).
Original entry on oeis.org
1, 6, 47, 420, 4059, 41316, 436345, 4737018, 52535950, 592667532, 6779699073, 78458218746, 916886214115, 10805128064100, 128260666769895, 1532180536574580, 18405744106135914, 222204347510440092, 2694506677864591810, 32804976554127379680, 400837173223351237295
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2+x)^2)/x)
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a(n) = sum(k=0, n, binomial(2*n+2, k)*binomial(4*n-2*k+4, n-k))/(n+1);
A369503
Expansion of (1/x) * Series_Reversion( x / ((1+x)^2+x^2)^2 ).
Original entry on oeis.org
1, 4, 24, 168, 1284, 10384, 87360, 756704, 6703168, 60444928, 552990592, 5120101760, 47887472000, 451759449600, 4293634467840, 41073654689280, 395170166443008, 3821262491103232, 37118973530660864, 362035991963869184, 3544080121528001536
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2+x^2)^2)/x)
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a(n) = sum(k=0, n\2, binomial(2*n+2, k)*binomial(4*n-2*k+4, n-2*k))/(n+1);
A369507
Expansion of (1/x) * Series_Reversion( x / ((1+x)^3+x^3)^2 ).
Original entry on oeis.org
1, 6, 51, 508, 5535, 63888, 767689, 9502254, 120324606, 1551362160, 20296839585, 268785905790, 3595951246855, 48528885742200, 659856371680971, 9031161933443468, 124319953470044970, 1720113658097639532, 23908612149570793386, 333680424238179500976
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^3+x^3)^2)/x)
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a(n) = sum(k=0, n\3, binomial(2*n+2, k)*binomial(6*n-3*k+6, n-3*k))/(n+1);
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