A371432
Expansion of (1/x) * Series_Reversion( x * ((1-x)^2 + x^4) ).
Original entry on oeis.org
1, 2, 7, 30, 142, 714, 3740, 20178, 111325, 625042, 3559101, 20502014, 119249277, 699330360, 4130235408, 24543145310, 146629131642, 880184547880, 5305961255490, 32107022363150, 194947974895960, 1187354222296110, 7252099548616320, 44408257163905050
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^2+x^4))/x)
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a(n) = sum(k=0, n\4, (-1)^k*binomial(n+k, k)*binomial(3*n-2*k+1, n-4*k))/(n+1);
A371433
Expansion of (1/x) * Series_Reversion( x * ((1-x)^3 + x) ).
Original entry on oeis.org
1, 2, 5, 11, 11, -77, -704, -3795, -15686, -48598, -74009, 376623, 4438840, 27458060, 126898948, 440550682, 849522927, -2621906045, -39993434701, -270428078305, -1339005344985, -5014789377825, -11407684195950, 18849058485855, 417417757017612, 3058172078113944
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^3+x))/x)
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a(n) = sum(k=0, n, (-1)^k*binomial(n+k, k)*binomial(4*n+2*k+2, n-k))/(n+1);
A371434
Expansion of (1/x) * Series_Reversion( x * ((1-x)^3 + x^2) ).
Original entry on oeis.org
1, 3, 14, 76, 444, 2702, 16840, 106389, 676566, 4307754, 27333384, 172040544, 1068547788, 6505380072, 38446578888, 217095119499, 1136270066490, 5125578859296, 15040187738184, -47786768551830, -1453703259770520, -18311261482519860, -186896777677695720
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^3+x^2))/x)
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a(n) = sum(k=0, n\2, (-1)^k*binomial(n+k, k)*binomial(4*n+k+2, n-2*k))/(n+1);
Showing 1-3 of 3 results.