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A002045
MacMahon's solid partitions of n in which 4 is the smallest summand.
1
10, 0, 0, 0, 55, 150, 210, 280, 580, 1275, 2905, 5350, 9985, 17965, 33665, 62895, 117287, 214610, 389805, 700720, 1259890, 2250405, 4008717, 7092366, 12497237, 21904825, 38253450, 66511772, 115230973, 198829023, 341874534, 585658726, 999965454, 1701581818, 2886406281
OFFSET
4,1
REFERENCES
R. Chandra, Tables of solid partitions, Proceedings of the Indian National Science Academy, 26 (1960), 134-139.
V. S. Nanda, Tables of solid partitions, Proceedings of the Indian National Science Academy, 19 (1953), 313-314.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
R. Chandra, Tables of solid partitions, Proceedings of the Indian National Science Academy, 26 (1960), 134-139. [Annotated scanned copy]
V. S. Nanda, Tables of solid partitions, Proceedings of the Indian National Science Academy, 19 (1953), 313-314. [From Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 25 2010]
V. S. Nanda, Tables of solid partitions, Proceedings of the Indian National Science Academy, 19 (1953), 313-314. [Annotated scanned copy]
FORMULA
G.f.: Product_{i>=4} (-1 * [i=4] + 1/(1 - x^i)^binomial(i+1,2)). - John Tyler Rascoe, Jan 04 2026
PROG
(PARI)
A_x(N) = {my(x='x+O('x^(N+1))); Vec(prod(r=4, N, 1/(1-x^r)^binomial(r+1, 2)-(r==4)))} \\ John Tyler Rascoe, Jan 04 2026
CROSSREFS
KEYWORD
nonn
EXTENSIONS
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 25 2010
a(36)-a(38) added and name made more specific by John Tyler Rascoe, Jan 04 2026
STATUS
approved