A361703
Constant term in the expansion of (1 + w + x + y + z + 1/(w*x*y*z))^n.
Original entry on oeis.org
1, 1, 1, 1, 1, 121, 721, 2521, 6721, 15121, 143641, 1302841, 7579441, 32586841, 113753641, 509068561, 3599319361, 25076993761, 142188273361, 662296228561, 2933770097881, 15581813723281, 99333170493481, 623696622059281, 3466773281312881, 17406784944114721
Offset: 0
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a(n) = sum(k=0, n\5, (4*k)!/k!^4*binomial(5*k, 4*k)*binomial(n, 5*k));
A274783
Diagonal of the rational function 1/(1 - (w*x*y*z + w*x*y + w*x*z + w*y*z + x*y*z)).
Original entry on oeis.org
1, 1, 1, 25, 121, 361, 3361, 24361, 116425, 790441, 6060121, 36888721, 238815721, 1760983225, 11968188961, 79763351305, 570661612585, 4040282139625, 27901708614985, 198090585115105, 1420583920034161, 10056659775872161, 71730482491962361, 517012699162717825, 3713833648541268121
Offset: 0
- Seiichi Manyama, Table of n, a(n) for n = 0..1000
- A. Bostan, S. Boukraa, J.-M. Maillard, J.-A. Weil, Diagonals of rational functions and selected differential Galois groups, arXiv preprint arXiv:1507.03227 [math-ph], 2015.
- S. Eger, On the Number of Many-to-Many Alignments of N Sequences, arXiv:1511.00622 [math.CO], 2015.
- Jacques-Arthur Weil, Supplementary Material for the Paper "Diagonals of rational functions and selected differential Galois groups"
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with(combinat):
seq(add((n+k)!/(k!^4*(n-3*k)!), k = 0..floor(n/3)), n = 0..20); # Peter Bala, Jan 27 2018
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my(x='x, y='y, z='z, w='w);
R = 1/(1-(w*x*y*z+w*x*y+w*x*z+w*y*z+x*y*z));
diag(n, expr, var) = {
my(a = vector(n));
for (i = 1, #var, expr = taylor(expr, var[#var - i + 1], n));
for (k = 1, n, a[k] = expr;
for (i = 1, #var, a[k] = polcoeff(a[k], k-1)));
return(a);
};
diag(20, R, [x,y,z,w])
A385606
Diagonal of the rational function 1/(1 - (v^3 + w^3 + x^3 + y^3 + z^3 + v*w*x*y*z)).
Original entry on oeis.org
1, 1, 1, 121, 721, 2521, 120121, 1262521, 7514641, 200655841, 2804296441, 23211542641, 443673670441, 7070369866561, 73192033638361, 1173608444069881, 19482750854113681, 235115468646608881, 3483568444035458401, 57574418930692099801, 769737183831483390601, 11118980118960559362001
Offset: 0
A385607
Diagonal of the rational function 1/(1 - (v^2 + w^2 + x^2 + y^2 + z^2 + v*w*x*y*z)).
Original entry on oeis.org
1, 1, 121, 721, 115921, 1254121, 175667521, 2723150641, 328524651841, 6553910658241, 694593264839761, 16751100559753561, 1592929589394223081, 44555491032952142881, 3872288533662063462481, 121957120480085202781681, 9836937778718128127534881, 341177468192261294809070401
Offset: 0
Showing 1-4 of 4 results.
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