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A329444 The sixth moments of the squared binomial coefficients; a(n) = Sum_{m=0..n} m^6*binomial(n, m)^2. 5
0, 1, 68, 1314, 18080, 197350, 1836792, 15233316, 115776768, 821760390, 5520171800, 35438827996, 219038609088, 1310833221724, 7629754810160, 43348888067400, 241117582878720, 1316197491501510, 7065439665315480, 37362065079691500, 194909773207512000, 1004374157379474420 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

H. W. Gould, Combinatorial Identities, 1972.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = binomial(2n,n)*n^3*(n^6 + 3n^5 - 13n^4 - 15n^3 + 30n^2 + 8n - 2)/((16n-8)*(2n-3)*(2n-5)).

MATHEMATICA

Table[Sum[m^6*(Binomial[n, m])^2, {m, 0, n}], {n, 21}]

PROG

(PARI) a(n) = sum(m=0, n, m^6*binomial(n, m)^2); \\ Jinyuan Wang, Nov 23 2019

CROSSREFS

Cf. A037966, A037972, A074334, A294486, A329521, A329913.

Sequence in context: A283575 A231060 A245875 * A230687 A337962 A231106

Adjacent sequences:  A329441 A329442 A329443 * A329445 A329446 A329447

KEYWORD

nonn

AUTHOR

Nikita D. Gogin, Nov 16 2019

STATUS

approved

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Last modified September 28 00:46 EDT 2021. Contains 347698 sequences. (Running on oeis4.)