A366184
G.f. A(x) satisfies A(x) = (1 + x*A(x)^3)/(1 - x)^3.
Original entry on oeis.org
1, 4, 21, 163, 1487, 14697, 153226, 1659338, 18483960, 210437161, 2437721418, 28640748192, 340473075541, 4087735789616, 49494986770104, 603699827411356, 7410709463933414, 91484338902961485, 1135029142529785303, 14145212892466682781, 176993823220824229047
Offset: 0
-
a(n) = sum(k=0, n, binomial(n+8*k+2, n-k)*binomial(3*k, k)/(2*k+1));
A366182
G.f. A(x) satisfies A(x) = 1/(1 - x)^3 + x*A(x)^3/(1 - x).
Original entry on oeis.org
1, 4, 19, 128, 1037, 9221, 86847, 851073, 8586951, 88598014, 930473246, 9913648325, 106891041270, 1164153791878, 12788021717902, 141518588447588, 1576271179332762, 17657110535606919, 198792746866201879, 2248222906227731856, 25529220583699163958
Offset: 0
-
a(n) = sum(k=0, n, binomial(n+6*k+2, n-k)*binomial(3*k, k)/(2*k+1));
A364624
G.f. satisfies A(x) = 1/(1-x)^3 + x*A(x)^4.
Original entry on oeis.org
1, 4, 22, 194, 2103, 25129, 318816, 4214724, 57419725, 800461033, 11363418314, 163708299724, 2387365301187, 35173224652637, 522752043513952, 7827979832083872, 117992516684761733, 1788819120580964014, 27258417705055812586, 417270970443908301926
Offset: 0
-
a(n) = sum(k=0, n, binomial(n+8*k+2, 9*k+2)*binomial(4*k, k)/(3*k+1));
A366183
G.f. A(x) satisfies A(x) = 1/(1 - x)^3 + x*A(x)^3/(1 - x)^2.
Original entry on oeis.org
1, 4, 20, 145, 1250, 11746, 116641, 1204039, 12790067, 138895021, 1535005454, 17207743738, 195197256289, 2236419124408, 25842382083071, 300822398531482, 3524358836945936, 41524956284752018, 491722951928324392, 5848997420625891294, 69854562522309219081
Offset: 0
-
a(n) = sum(k=0, n, binomial(n+7*k+2, n-k)*binomial(3*k, k)/(2*k+1));
A366697
G.f. satisfies A(x) = (1 + x)^3 + x*A(x)^3.
Original entry on oeis.org
1, 4, 15, 94, 706, 5769, 49923, 449376, 4164228, 39459852, 380594767, 3724049805, 36876008673, 368835076813, 3720863181033, 37815675159285, 386818379566749, 3979362306753315, 41144521893563511, 427335033811660713, 4456402044181677264
Offset: 0
-
a(n) = sum(k=0, n, binomial(3*(2*k+1), n-k)*binomial(3*k, k)/(2*k+1));
A369691
G.f. satisfies A(x) = 1/(1-x)^3 + x^3*A(x)^3.
Original entry on oeis.org
1, 3, 6, 11, 24, 66, 196, 576, 1692, 5110, 15933, 50604, 161988, 521700, 1693362, 5541679, 18260055, 60487659, 201272437, 672550158, 2256204327, 7596059333, 25655943417, 86904524289, 295154911774, 1004906765178, 3429178160346, 11726499288028, 40178538608682
Offset: 0
-
a(n) = sum(k=0, n\3, binomial(n+3*k+2, n-3*k)*binomial(3*k, k)/(2*k+1));
Showing 1-6 of 6 results.