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 A183235 Sums of the cubes of multinomial coefficients. 8
 1, 1, 9, 244, 15833, 1980126, 428447592, 146966837193, 75263273895385, 54867365927680618, 54868847079435960134, 73030508546599681432983, 126197144644287414997433576, 277255161467330877411064074059 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Equals sums of the cubes of terms in rows of the triangle of multinomial coefficients (A036038). Ignoring initial term, equals the logarithmic derivative of A182963. LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..180 FORMULA G.f.: Sum_{n>=0} a(n)*x^n/n!^3 = Product_{n>=1} 1/(1 - x^n/n!^3). a(n) ~ c * (n!)^3, where c = Product_{k>=2} 1/(1-1/(k!)^3) = 1.14825648754771664323845829539510031170864046029463094659207423270573478812675... . - Vaclav Kotesovec, Feb 19 2015 EXAMPLE G.f.: A(x) = 1 + x + 9*x^2/2!^3 + 244*x^3/3!^3 + 15833*x^4/4!^3 +... A(x) = 1/((1-x)*(1-x^2/2!^3)*(1-x^3/3!^3)*(1-x^4/4!^3)*...). ... After the initial term a(0)=1, the next few terms are a(1) = 1^3 = 1, a(2) = 1^3 + 2^3 = 9, a(3) = 1^3 + 3^3 + 6^3 = 244, a(4) = 1^3 + 4^3 + 6^3 + 12^3 + 24^3 = 15833, a(5) = 1^3 + 5^3 + 10^3 + 20^3 + 30^3 + 60^3 + 120^3 = 1980126, ...; and continue with the sums of cubes of the terms in triangle A036038. PROG (PARI) {a(n)=n!^3*polcoeff(1/prod(k=1, n, 1-x^k/k!^3 +x*O(x^n)), n)} CROSSREFS Cf. A036038, A005651, A183240, A183236, A183237, A183238; A182963. Sequence in context: A112028 A368769 A329305 * A359732 A259673 A272234 Adjacent sequences: A183232 A183233 A183234 * A183236 A183237 A183238 KEYWORD nonn AUTHOR Paul D. Hanna, Jan 04 2011 EXTENSIONS Examples added and name changed by Paul D. Hanna, Jan 05 2011 STATUS approved

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Last modified July 21 06:08 EDT 2024. Contains 374463 sequences. (Running on oeis4.)