A371483
G.f. A(x) satisfies A(x) = 1 / (1 - x*A(x) / (1-x))^3.
Original entry on oeis.org
1, 3, 18, 124, 933, 7446, 61943, 531348, 4666425, 41751325, 379230711, 3487769871, 32414437521, 303950138604, 2872137458010, 27322233357964, 261446381792670, 2514851398148595, 24303030755342128, 235841264063844258, 2297278004837062317
Offset: 0
-
a(n) = sum(k=0, n, binomial(n-1, n-k)*binomial(4*k+2, k)/(k+1));
A371517
G.f. A(x) satisfies A(x) = (1 + x*A(x) / (1-x))^4.
Original entry on oeis.org
1, 4, 26, 188, 1459, 11892, 100444, 871528, 7722557, 69590628, 635807180, 5876094308, 54836925779, 516029817620, 4891147100886, 46653935716492, 447490869463145, 4313492172957396, 41763413498670702, 405968522259130636, 3960526930400038404
Offset: 0
-
a(n) = 4*sum(k=0, n, binomial(n-1, n-k)*binomial(4*k+3, k)/(3*k+4));
A371519
G.f. A(x) satisfies A(x) = 1 / (1 - x*A(x) / (1-x))^5.
Original entry on oeis.org
1, 5, 45, 470, 5375, 65231, 825225, 10764185, 143739440, 1955340360, 27001732972, 377530388235, 5333865386885, 76031188364860, 1092117166466660, 15792298241897649, 229704197116753825, 3358528175751886765, 49333470827844265285, 727680248026484478405
Offset: 0
-
a(n) = sum(k=0, n, binomial(n-1, n-k)*binomial(6*k+4, k)/(k+1));
A371520
G.f. A(x) satisfies A(x) = (1 + x*A(x) / (1-x))^5.
Original entry on oeis.org
1, 5, 40, 360, 3495, 35726, 378965, 4133080, 46059020, 522196465, 6004261226, 69849651025, 820651943130, 9723556336780, 116056250171385, 1394082307995626, 16840510019954835, 204453614350921540, 2493311080293185200, 30528431677508637205, 375155454309681439001
Offset: 0
-
a(n) = 5*sum(k=0, n, binomial(n-1, n-k)*binomial(5*k+4, k)/(4*k+5));
A378610
Expansion of (1/x) * Series_Reversion( x * (1 - x/(1 - x))^4 ).
Original entry on oeis.org
1, 4, 30, 276, 2825, 30884, 353108, 4170500, 50485764, 623084056, 7810707894, 99175174284, 1272856327470, 16486135484248, 215212582153840, 2828658852385572, 37401956484705132, 497174193516767600, 6640063367021736728, 89058042321373540912, 1199031374607501831273
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x/(1-x))^4)/x)
-
a(n, s=1, t=4, u=-4) = 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);
A371583
G.f. satisfies A(x) = ( 1 + x*A(x)^(5/2) / (1 - x) )^2.
Original entry on oeis.org
1, 2, 13, 104, 940, 9166, 94044, 1000602, 10939780, 122161128, 1387361151, 15974899766, 186069556707, 2188416960148, 25953579753464, 310022550197360, 3726709235290628, 45047517497268968, 547217895030263028, 6676784544374859088, 81789906534091716353
Offset: 0
-
a(n, r=2, s=1, t=5, u=0) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));
A370695
G.f. A(x) satisfies A(x) = (1 + x*A(x)^(3/4) / (1-x))^4.
Original entry on oeis.org
1, 4, 22, 128, 777, 4872, 31330, 205560, 1370868, 9266104, 63343006, 437183260, 3042337215, 21323543252, 150395596016, 1066637271424, 7602188660799, 54422262148632, 391146728466980, 2821396586367568, 20417766975784066, 148200184917042112
Offset: 0
-
A370695 := proc(n)
4*add(binomial(n-1,n-k)*binomial(3*k+4,k)/(3*k+4),k=0..n) ;
end proc:
seq(A370695(n),n=0..80) ; #R. J. Mathar, Oct 24 2024
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a(n) = 4*sum(k=0, n, binomial(n-1, n-k)*binomial(3*k+4, k)/(3*k+4));
Showing 1-7 of 7 results.