A365178
G.f. satisfies A(x) = 1 + x*A(x)^4*(1 + x).
Original entry on oeis.org
1, 1, 5, 30, 210, 1595, 12791, 106574, 913562, 8004861, 71375653, 645536234, 5907683486, 54605672300, 509043322720, 4780441915832, 45182744331388, 429472919087158, 4102806757542542, 39370967793387086, 379335734835510622, 3668220243145708341
Offset: 0
-
a(n) = sum(k=0, n, binomial(k, n-k)*binomial(4*k, k)/(3*k+1));
A365183
G.f. satisfies A(x) = 1 + x*A(x)^4*(1 + x*A(x)^4).
Original entry on oeis.org
1, 1, 5, 34, 268, 2299, 20838, 196326, 1903524, 18868861, 190356231, 1948055058, 20173907384, 211020478270, 2226243632838, 23660868061422, 253099278807684, 2722819049879436, 29439894433161189, 319749417998303470, 3486914150183526920
Offset: 0
-
a(n) = sum(k=0, n\2, binomial(n-k, k)*binomial(4*n+1, n-k))/(4*n+1);
A365180
G.f. satisfies A(x) = 1 + x*A(x)^4*(1 + x*A(x)).
Original entry on oeis.org
1, 1, 5, 31, 223, 1740, 14328, 122549, 1078197, 9695359, 88710199, 823247686, 7730244098, 73310150097, 701163085849, 6755544043969, 65506554804129, 638794412442172, 6260571309256152, 61632794482411367, 609197871548209907, 6043456939539775056
Offset: 0
-
a(n) = sum(k=0, n, binomial(n+3*k+1, k)*binomial(k, n-k)/(n+3*k+1));
A365181
G.f. satisfies A(x) = 1 + x*A(x)^4*(1 + x*A(x)^2).
Original entry on oeis.org
1, 1, 5, 32, 237, 1905, 16160, 142392, 1290613, 11955947, 112697701, 1077438356, 10422562156, 101827196684, 1003312506776, 9958506719664, 99479743121349, 999370184665407, 10090067735619023, 102330789530653912, 1041997707624103589, 10648963961114066129
Offset: 0
-
a(n) = sum(k=0, n, binomial(2*n+2*k+1, k)*binomial(k, n-k)/(2*n+2*k+1));
A367041
G.f. satisfies A(x) = 1 + x^2 + x*A(x)^4.
Original entry on oeis.org
1, 1, 5, 26, 168, 1195, 8988, 70318, 566388, 4665221, 39113732, 332691758, 2863778072, 24900264326, 218372530380, 1929363592870, 17157018725000, 153442147343648, 1379250344938676, 12453816724761706, 112907775890596400, 1027394297869071687
Offset: 0
-
a(n) = sum(k=0, n\2, binomial(3*(n-2*k)+1, k)*binomial(4*(n-2*k), n-2*k)/(3*(n-2*k)+1));
A368963
Expansion of (1/x) * Series_Reversion( x * (1-x-x^2)^3 ).
Original entry on oeis.org
1, 3, 18, 130, 1044, 8949, 80201, 742365, 7042215, 68103156, 668913195, 6654654240, 66916523202, 679039933050, 6944796387690, 71512538784330, 740800257667236, 7714659988543299, 80719544259082000, 848155028673449400, 8945940728543188656
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x-x^2)^3)/x)
-
a(n, s=2, t=3, 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);
A367048
G.f. satisfies A(x) = 1 + x*A(x)^4 + x^2*A(x).
Original entry on oeis.org
1, 1, 5, 27, 177, 1270, 9645, 76206, 619913, 5156959, 43667985, 375140383, 3261467573, 28641957520, 253702185717, 2263964868768, 20334261430769, 183680693283325, 1667613040080061, 15208587941854251, 139266058402655669, 1279953660931370623
Offset: 0
-
a(n) = sum(k=0, n\2, binomial(3*n-5*k+1, k)*binomial(4*n-7*k, n-2*k)/(3*n-5*k+1));
A367049
G.f. satisfies A(x) = 1 + x*A(x)^4 + x^2*A(x)^2.
Original entry on oeis.org
1, 1, 5, 28, 187, 1361, 10479, 83914, 691738, 5830903, 50028259, 435454040, 3835732631, 34128555184, 306276957665, 2769050552948, 25197515469820, 230599623819217, 2121066298440282, 19597929365099640, 181814132152022195, 1692920612932871541
Offset: 0
-
a(n) = sum(k=0, n\2, binomial(3*n-4*k+1, k)*binomial(4*n-6*k, n-2*k)/(3*n-4*k+1));
A367050
G.f. satisfies A(x) = 1 + x*A(x)^4 + x^2*A(x)^3.
Original entry on oeis.org
1, 1, 5, 29, 198, 1469, 11518, 93875, 787392, 6752175, 58929541, 521718814, 4674070602, 42296077935, 386027716280, 3549332631052, 32845586854208, 305685481682970, 2859315003009776, 26866125820982711, 253457922829307765, 2399910588283502630
Offset: 0
-
a(n) = sum(k=0, n\2, binomial(3*n-3*k+1, k)*binomial(4*n-5*k, n-2*k)/(3*n-3*k+1));
Showing 1-9 of 9 results.