The sum of the series ∑n=1∞n2+6n+10(2n+1)! is equal to

∑n=1∞n2+6n+10(2n+1)!   Let 2n+1=λ  ⇒n=λ-12n2+6n+10(2n+1)!=λ-122+6λ-12+10λ!=λ2+10λ+294(λ!) Also λ=3,5,7,9,11,……∴ Required =14∑λ(λ-1)+11λ+29λ!λ=3,5,7,……….=14∑λ=3,5,7,…1(λ-2)!+11(λ-1)!+29λ!=1414+1⌊3+12+….+111⌊2+14+…..++291⌊3+115+117+……=14e-1e2+11e+1e-22+29e-1e-22  =1841e-19c-80