A360709
Expansion of Sum_{k>=0} (x^3 / (1 - k*x))^k.
Original entry on oeis.org
1, 0, 0, 1, 1, 1, 2, 5, 13, 34, 90, 247, 720, 2256, 7568, 26814, 98982, 377541, 1484254, 6021789, 25271173, 109850447, 494355359, 2298362532, 11008133629, 54175202125, 273460921605, 1414449612648, 7494262602464, 40669492399396
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, (x^3/(1-k*x))^k))
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a(n) = if(n==0, 1, sum(k=1, n\3, k^(n-3*k)*binomial(n-2*k-1, k-1)));
A360814
Expansion of Sum_{k>=0} x^(2*k) / (1 - k*x)^(k+1).
Original entry on oeis.org
1, 0, 1, 2, 4, 10, 30, 98, 338, 1240, 4877, 20496, 91213, 426678, 2090081, 10702438, 57193760, 318283388, 1840036058, 11026424446, 68370955450, 438039068726, 2896018310881, 19733372875632, 138418266287689, 998363508783924, 7396739279819185, 56239695790595786
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, x^(2*k)/(1-k*x)^(k+1)))
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a(n) = sum(k=0, n\2, k^(n-2*k)*binomial(n-k, k));
A360818
Expansion of Sum_{k>=0} ( (k*x)^2 / (1 - k*x) )^k.
Original entry on oeis.org
1, 0, 1, 1, 17, 65, 922, 7074, 106183, 1248479, 21144289, 331763177, 6441011484, 124904347404, 2773880604749, 63538143151589, 1600211849569585, 42076439530000297, 1189408501356380558, 35214128238218917974, 1106088535644470694779
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, ((k*x)^2/(1-k*x))^k))
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a(n) = sum(k=0, n\2, k^n*binomial(n-k-1, n-2*k));
Showing 1-3 of 3 results.