A007280 Multiplicative encoding of partition triangle. (Formerly M1694)

2, 6, 30, 630, 34650, 47297250, 309560501250, 618190773193743750, 66537433850544954015468750, 65572844234095125006030612749369531250, 70740128442809835497514843888197127919441136894531250, 1246818779086736832640424654624124149208275677194466874759034601214355468750

Offset

1,1

References

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 307.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..12.

N. J. A. Sloane, An on-line version of the Encyclopedia of Integer Sequences, Electronic J. Combinatorics, Vol. 1, no. 1, 1994.

Formula

a(n) = Product_{k=1..n} prime(k)^A008284(n,k). - Sean A. Irvine, Dec 03 2017; corrected by Michel Marcus, Nov 18 2025

Prog

(PARI) a(n) = prod(k=1, n, prime(k)^#partitions(n-k, k)); \\ Michel Marcus, Nov 18 2025

Crossrefs

Cf. A000040.

Sequence in context: A326867 A320830 A074777 * A280260 A102927 A376399

Adjacent sequences: A007277 A007278 A007279 * A007281 A007282 A007283

Keyword

nonn

Author

N. J. A. Sloane

Extensions

a(11) from Sean A. Irvine, Dec 03 2017

a(12) from Michel Marcus, Nov 18 2025

Status

approved