A336622 a(n) = Sum_{k=0..n} Sum_{i=0..k} Sum_{j=0..i} (binomial(n,k) * binomial(k,i) * binomial(i,j))^n.

1, 4, 28, 1192, 591460, 3441637504, 219272057247376, 185528149944660881488, 2405748000504972140803769860, 349789137657321307953339196885516144, 652520795984468974632890750361094911319873648

Offset: 0

Author

Ilya Gutkovskiy, Jul 29 2020

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..42

Crossrefs

Cf. A000302, A002895, A167010, A287699, A336270.

Programs

Magma

B:=Binomial; [(&+[(&+[(&+[(B(n,j)*B(n-j,k-j)*B(k-j,k-i))^n: j in [0..i]]): i in [0..k]]): k in [0..n]]): n in [0..20]]; // G. C. Greubel, Aug 31 2022

Mathematica

Table[Sum[Sum[Sum[(Binomial[n, k] Binomial[k, i] Binomial[i, j])^n, {j, 0, i}], {i, 0, k}], {k, 0, n}], {n, 0, 10}]
Table[(n!)^n SeriesCoefficient[Sum[x^k/(k!)^n, {k, 0, n}]^4, {x, 0, n}], {n, 0, 10}]

SageMath

b=binomial
def A336622(n): return sum(sum(sum( (b(n,j)*b(n-j,k-j)*b(k-j,k-i))^n for j in (0..i)) for i in (0..k)) for k in (0..n))
[A336622(n) for n in (0..20)] # G. C. Greubel, Aug 31 2022

Formula

a(n) = (n!)^n * [x^n] (Sum_{k>=0} x^k / (k!)^n)^4.