A369212
Expansion of (1/x) * Series_Reversion( x / ((1+x)^2+x^3) ).
Original entry on oeis.org
1, 2, 5, 15, 50, 177, 652, 2473, 9594, 37892, 151846, 615859, 2523217, 10427471, 43415259, 181941198, 766841846, 3248517320, 13823977350, 59067577266, 253315964424, 1089998388418, 4704475230340, 20361365646315, 88351705071583, 384280788724692, 1675063399090659
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2+x^3))/x)
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a(n) = sum(k=0, n\3, binomial(n+1, k)*binomial(2*n-2*k+2, n-3*k))/(n+1);
A369159
Expansion of (1/x) * Series_Reversion( x / ((1+x)^3+x^4) ).
Original entry on oeis.org
1, 3, 12, 55, 274, 1443, 7905, 44593, 257305, 1511553, 9010170, 54361486, 331336454, 2037132958, 12619056108, 78682008194, 493427982703, 3110202012353, 19693920616872, 125214061831251, 799059649687239, 5116372686471627, 32860439054510610
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^3+x^4))/x)
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a(n) = sum(k=0, n\4, binomial(n+1, k)*binomial(3*n-3*k+3, n-4*k))/(n+1);
A371427
Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 - x^4) ).
Original entry on oeis.org
1, 2, 5, 14, 41, 122, 363, 1066, 3046, 8300, 20791, 43738, 51297, -174406, -1825027, -10480330, -50143510, -218385772, -895007802, -3504952380, -13214355159, -48116028934, -169216483595, -573113441834, -1856620607526, -5675964306988, -15927363432481
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+1, k)*binomial(2*n-2*k+2, n-4*k))/(n+1);
Showing 1-3 of 3 results.