A347844 a(n) is the number of (strict) chains of subspaces with ends 0 and (F_7)^n.

1, 9, 571, 254451, 793949053, 17342194001493, 2651651342949844915, 2838097493373982791359403, 21263575996354049430406053548413, 1115175826296921591259255638404605916661, 409400558616252174531470888061523725583206190339

Offset: 1

Author

Álvar Ibeas, Sep 15 2021

Keywords

• nonn

Examples

			a(3) = 571 = 1 * 1 + 57 * 2 + 456 * 1, counting:
the unrefined chain 0 < (F_7)^3;
57 chains 0 < V < (F_7)^3, with dim(V) = 1; another
57 chains 0 < V < (F_7)^3, with dim(V) = 2; and
456 chains 0 < V_1 < V_2 < (F_7)^3.
		

Links

• Álvar Ibeas, Table of n, a(n) for n = 1..40

Crossrefs

Cf. A289545, A347489, A036038.

Column k=7 of A381426.

Formula

a(n) = Sum_{L partition of n} A347489(n, L) * A036038(len(L), sig(L)), where sig(L) is the partition composed by the part multiplicities of L.