A336270 a(n) = Sum_{k=0..n} Sum_{j=0..k} (binomial(n,k) * binomial(k,j))^n.

1, 3, 15, 381, 67635, 83118753, 813824623689, 58040410068847251, 32150480245981639533315, 154935057570894645075940703673, 5474671509704049919709361235659936825, 1600436120524545216094358662984789029130593831

Offset: 0

Author

Ilya Gutkovskiy, Jul 15 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..47

Crossrefs

Cf. A000244, A002893, A141057, A167010, A172434, A180350.

Programs

Mathematica

Table[Sum[Sum[(Binomial[n, k] Binomial[k, j])^n, {j, 0, k}], {k, 0, n}], {n, 0, 11}]
Table[(n!)^n SeriesCoefficient[Sum[x^k/(k!)^n, {k, 0, n}]^3, {x, 0, n}], {n, 0, 11}]

PARI

a(n) = sum(k=0, n, sum(j=0, k, (binomial(n,k) * binomial(k,j))^n)); \\ Michel Marcus, Jul 16 2020

Formula

a(n) = (n!)^n * [x^n] (Sum_{k>=0} x^k / (k!)^n)^3.