A368961
Expansion of (1/x) * Series_Reversion( x * (1-x-x^2)^2 ).
Original entry on oeis.org
1, 2, 9, 48, 286, 1820, 12116, 83334, 587537, 4223582, 30840355, 228111390, 1705509981, 12868775056, 97867753424, 749401318160, 5772939358590, 44708058004740, 347879528717526, 2718400037837988, 21323471768334120, 167844335760482220, 1325332432687278960
Offset: 0
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a[n_] := (1/(n+1)) * Sum[Binomial[2*n+k+1,k] * Binomial[3*n-k+1,n-2*k],{k,0,Floor[n/2]}]; Array[a,23,0] (* Stefano Spezia, Aug 11 2025 *)
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x-x^2)^2)/x)
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a(n, s=2, t=2, u=0) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
A368966
Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x-x^3)^2 ).
Original entry on oeis.org
1, 3, 15, 93, 644, 4769, 36953, 295867, 2428373, 20322566, 172759032, 1487632887, 12948891408, 113748663495, 1007117650350, 8978151790011, 80519598139947, 725976573163011, 6576546244337046, 59829384514916820, 546375444906314661, 5006934930385254672
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)*(1-x-x^3)^2)/x)
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a(n, s=3, t=2, u=1) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
A368967
Expansion of (1/x) * Series_Reversion( x * (1-x)^2 * (1-x-x^2)^2 ).
Original entry on oeis.org
1, 4, 28, 238, 2244, 22568, 237199, 2574276, 28627224, 324503718, 3735672880, 43555658640, 513277420803, 6103767231712, 73153216133600, 882708243017414, 10714917867247020, 130752597362068496, 1603069096165788706, 19737123968746454284, 243930175282166574432
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^2*(1-x-x^2)^2)/x)
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a(n, s=2, t=2, u=2) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
A368973
Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x+x^2)^2 ).
Original entry on oeis.org
1, 3, 13, 65, 351, 1989, 11650, 69903, 427225, 2649229, 16622079, 105310673, 672687322, 4327037010, 28002409452, 182179075689, 1190778886791, 7815755146095, 51491064226095, 340374137775879, 2256891800364421, 15006481967365535, 100037043223408890
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)*(1-x+x^2)^2)/x)
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a(n, s=2, t=2, u=1) = sum(k=0, n\s, (-1)^k*binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
A369486
Expansion of (1/x) * Series_Reversion( x / (1-x) * (1-x-x^2)^2 ).
Original entry on oeis.org
1, 1, 4, 15, 67, 314, 1547, 7865, 41004, 217953, 1176832, 6436676, 35587416, 198569471, 1116741601, 6323669519, 36024382515, 206315985386, 1187205083042, 6860598312545, 39797882898452, 231666709974264, 1352813494962672, 7922553881534274, 46520280837291427
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1-x)*(1-x-x^2)^2)/x)
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a(n, s=2, t=2, u=1) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t-u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
A372458
Coefficient of x^n in the expansion of 1 / ( (1-x) * (1-x-x^2)^2 )^n.
Original entry on oeis.org
1, 3, 25, 225, 2129, 20723, 205471, 2063890, 20931585, 213864939, 2198044805, 22699471171, 235354244255, 2448409104820, 25544033624414, 267158874185420, 2800191197529633, 29405702263792875, 309320021637262225, 3258658594126096867, 34376186445159365709
Offset: 0
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a(n, s=2, t=2, u=1) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((t+u+1)*n-(s-1)*k-1, n-s*k));
Showing 1-6 of 6 results.