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 A103929 Number of partitions of n into parts but with two kinds of parts of sizes 1 to 10. 2
 1, 2, 5, 10, 20, 36, 65, 110, 185, 300, 481, 751, 1162, 1762, 2647, 3918, 5748, 8331, 11981, 17056, 24108, 33787, 47043, 65019, 89336, 121954, 165585, 223542, 300295, 401331, 533937, 707057, 932404, 1224376, 1601571, 2086851, 2709449, 3505228 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS See A103923 for other combinatorial interpretations of a(n). In general, column m of A008951 is asymptotic to exp(Pi*sqrt(2*n/3)) * 6^(m/2) * n^((m-2)/2) / (4*sqrt(3) * m! * Pi^m), equivalently to 6^(m/2) * n^(m/2) / (m! * Pi^m) * p(n), where p(n) is the partition function A000041. - Vaclav Kotesovec, Aug 28 2015 REFERENCES H. Gupta et al., Tables of Partitions. Royal Society Mathematical Tables, Vol. 4, Cambridge Univ. Press, 1958 (reprinted 1962), p. 91. J. Riordan, Combinatorial Identities, Wiley, 1968, p. 199. LINKS FORMULA G.f.: (product(1/(1-x^k), k=1..10)^2)*product(1/(1-x^j), j=11..infty). a(n)=sum(A103924(n-10*j), j=0..floor(n/10)), n>=0. a(n) ~ exp(Pi*sqrt(2*n/3)) * 6^5 * n^4 / (4*sqrt(3) * 10! * Pi^10). - Vaclav Kotesovec, Aug 28 2015 MATHEMATICA nmax=60; CoefficientList[Series[Product[1/(1-x^k), {k, 1, 10}] * Product[1/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 28 2015 *) Table[Length@IntegerPartitions[n, All, Range@n~Join~Range@10], {n, 0, 37}] (* Robert Price, Jul 29 2020 *) CROSSREFS Eleventh column (m=10) of Fine-Riordan triangle A008951 and of triangle A103923, i.e. the p_2(n, m) array of the Gupta et al. reference. Cf. A000712 (all parts of two kinds). Sequence in context: A103926 A103927 A103928 * A121597 A000712 A032442 Adjacent sequences:  A103926 A103927 A103928 * A103930 A103931 A103932 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Mar 24 2005 STATUS approved

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Last modified April 16 10:20 EDT 2021. Contains 343036 sequences. (Running on oeis4.)