A364629
G.f. satisfies A(x) = (1+x*A(x)^3)/(1-x)^2.
Original entry on oeis.org
1, 3, 14, 94, 735, 6239, 55888, 520028, 4977321, 48689260, 484623552, 4892304686, 49971163021, 515496741918, 5363023614620, 56204877993184, 592811175777029, 6287909183751105, 67029933733468729, 717749621979800340, 7716543390041275964
Offset: 0
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a(n) = sum(k=0, n, binomial(n+5*k+1, 6*k+1)*binomial(3*k, k)/(2*k+1));
A162476
Expansion of (1/(1-x))*c(x/(1-x)^4), c(x) the g.f. of A000108.
Original entry on oeis.org
1, 2, 8, 39, 205, 1136, 6548, 38882, 236260, 1462131, 9184413, 58408588, 375330536, 2433325315, 15896742423, 104546968252, 691608993478, 4599024778431, 30724413312953, 206114347293697, 1387917616331135, 9377747277136328
Offset: 0
A363816
G.f. satisfies A(x) = (1 + x/A(x))/(1 - x)^2.
Original entry on oeis.org
1, 3, 2, 8, -9, 62, -230, 1054, -4753, 22208, -105419, 508396, -2482284, 12248430, -60980860, 305955372, -1545397447, 7852100312, -40105277621, 205798130624, -1060467961487, 5485199090834, -28469067353663, 148220323891484, -773892318396664, 4051261817405034
Offset: 0
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A363816[n_]:=(-1)^(n-1)Sum[Binomial[2k-1,k]Binomial[2(k-1),n-k]/(2k-1),{k,0,n}];Array[A363816,30,0] (* Paolo Xausa, Oct 20 2023 *)
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a(n) = (-1)^(n-1)*sum(k=0, n, binomial(2*k-1, k)*binomial(2*(k-1), n-k)/(2*k-1));
A364630
G.f. satisfies A(x) = (1+x*A(x)^4)/(1-x)^2.
Original entry on oeis.org
1, 3, 17, 153, 1621, 18732, 229103, 2915498, 38204497, 512027945, 6985933889, 96705749625, 1354868839933, 19175008086962, 273731258980839, 3936883123412972, 56991044183321197, 829750943505927435, 12142121554514962205, 178488780583916045949
Offset: 0
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a(n) = sum(k=0, n, binomial(n+7*k+1, 8*k+1)*binomial(4*k, k)/(3*k+1));
A363818
G.f. satisfies A(x) = (1 + x/A(x)^2)/(1 - x)^2.
Original entry on oeis.org
1, 3, -1, 24, -125, 924, -6895, 54181, -438737, 3639655, -30769033, 264122781, -2296010693, 20171456222, -178818115155, 1597550237324, -14369097515939, 130010781029079, -1182520161325459, 10806114831458755, -99163805247182631, 913441732959868748
Offset: 0
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a(n) = (-1)^(n-1)*sum(k=0, n, binomial(3*k-1, k)*binomial(2*(2*k-1), n-k)/(3*k-1));
A376159
G.f. satisfies A(x) = 1 / ((1-x)^3 - x*A(x)).
Original entry on oeis.org
1, 4, 17, 90, 539, 3451, 23100, 159720, 1131905, 8178326, 60019533, 446166771, 3352530190, 25422458170, 194302002463, 1495223230621, 11575504625874, 90090318248607, 704480581789900, 5532228951823605, 43610427926723780, 344972119634359080, 2737451123900901555
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(2/((1-x)^3+sqrt((1-x)^6-4*x)))
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a(n) = sum(k=0, n, binomial(n+5*k+2, n-k)*binomial(2*k, k)/(k+1));
Showing 1-6 of 6 results.
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